diff --git a/changelog.d/pr-190.md b/changelog.d/pr-190.md
new file mode 100644
index 00000000..05e291b6
--- /dev/null
+++ b/changelog.d/pr-190.md
@@ -0,0 +1,3 @@
+### 🚀 Enhancements and New Features
+
+- Add `--extra-inputs` to `containers-add`.  Fixes [#189](https://github.com/datalad/datalad-container/issues/189) via [PR #190](https://github.com/datalad/datalad-container/pull/190) (by [@nobodyinperson](https://github.com/nobodyinperson))
diff --git a/datalad_container/containers_add.py b/datalad_container/containers_add.py
index fbba420f..2c2b69b9 100644
--- a/datalad_container/containers_add.py
+++ b/datalad_container/containers_add.py
@@ -140,11 +140,29 @@ class ContainersAdd(Interface):
             this container, e.g. "singularity exec {img} {cmd}". Where '{img}'
             is a placeholder for the path to the container image and '{cmd}' is
             replaced with the desired command. Additional placeholders:
-            '{img_dspath}' is relative path to the dataset containing the image.
+            '{img_dspath}' is relative path to the dataset containing the image,
+            '{img_dirpath}' is the directory containing the '{img}'.
             """,
             metavar="FORMAT",
             constraints=EnsureStr() | EnsureNone(),
         ),
+        extra_input=Parameter(
+            args=("--extra-input",),
+            doc="""Additional file the container invocation depends on (e.g.
+            overlays used in --call-fmt). Can be specified multiple times.
+            Similar to --call-fmt, the placeholders {img_dspath} and
+            {img_dirpath} are available. Will be stored in the dataset config and
+            later added alongside the container image to the `extra_inputs`
+            field in the run-record and thus automatically be fetched when
+            needed.
+            """,
+            action="append",
+            default=[],
+            metavar="FILE",
+            # Can't use EnsureListOf(str) yet as it handles strings as iterables...
+            # See this PR: https://github.com/datalad/datalad/pull/7267
+            # constraints=EnsureListOf(str) | EnsureNone(),
+        ),
         image=Parameter(
             args=("-i", "--image"),
             doc="""Relative path of the container image within the dataset. If not
@@ -168,7 +186,7 @@ class ContainersAdd(Interface):
     @datasetmethod(name='containers_add')
     @eval_results
     def __call__(name, url=None, dataset=None, call_fmt=None, image=None,
-                 update=False):
+                 update=False, extra_input=None):
         if not name:
             raise InsufficientArgumentsError("`name` argument is required")
 
@@ -321,6 +339,28 @@ def __call__(name, url=None, dataset=None, call_fmt=None, image=None,
                 "{}.cmdexec".format(cfgbasevar),
                 call_fmt,
                 force=True)
+        # --extra-input sanity check
+        # TODO: might also want to do that for --call-fmt above?
+        extra_input_placeholders = dict(img_dirpath="", img_dspath="")
+        for xi in (extra_input or []):
+            try:
+                xi.format(**extra_input_placeholders)
+            except KeyError as exc:
+                yield get_status_dict(
+                    action="containers_add", ds=ds, logger=lgr,
+                    status="error",
+                    message=("--extra-input %r contains unknown placeholder %s. "
+                             "Available placeholders: %s",
+                             repr(xi), exc, ', '.join(extra_input_placeholders)))
+                return
+
+        # actually setting --extra-input config
+        cfgextravar = "{}.extra-input".format(cfgbasevar)
+        if ds.config.get(cfgextravar) is not None:
+            ds.config.unset(cfgextravar)
+        for xi in (extra_input or []):
+            ds.config.add(cfgextravar, xi)
+
         # store changes
         to_save.append(op.join(".datalad", "config"))
         for r in ds.save(
diff --git a/datalad_container/containers_run.py b/datalad_container/containers_run.py
index 7c45f621..50de78db 100644
--- a/datalad_container/containers_run.py
+++ b/datalad_container/containers_run.py
@@ -11,6 +11,7 @@
 from datalad.distribution.dataset import datasetmethod
 from datalad.distribution.dataset import require_dataset
 from datalad.interface.base import eval_results
+from datalad.utils import ensure_iter
 
 from datalad.interface.results import get_status_dict
 from datalad.core.local.run import (
@@ -114,6 +115,7 @@ def __call__(cmd, container_name=None, dataset=None,
                     img=image_path,
                     cmd=cmd,
                     img_dspath=image_dspath,
+                    img_dirpath=op.dirname(image_path) or ".",
                 )
                 cmd = callspec.format(**cmd_kwargs)
             except KeyError as exc:
@@ -131,6 +133,28 @@ def __call__(cmd, container_name=None, dataset=None,
             # just prepend and pray
             cmd = container['path'] + ' ' + cmd
 
+        extra_inputs = []
+        for extra_input in ensure_iter(container.get("extra-input",[]), set):
+            try:
+                xi_kwargs = dict(
+                    img_dspath=image_dspath,
+                    img_dirpath=op.dirname(image_path) or ".",
+                )
+                extra_inputs.append(extra_input.format(**xi_kwargs))
+            except KeyError as exc:
+                yield get_status_dict(
+                    'run',
+                    ds=ds,
+                    status='error',
+                    message=(
+                        'Unrecognized extra_input placeholder: %s. '
+                        'See containers-add for information on known ones: %s',
+                        exc,
+                        ", ".join(xi_kwargs)))
+                return
+
+        lgr.debug("extra_inputs = %r", extra_inputs)
+
         with patch.dict('os.environ',
                         {CONTAINER_NAME_ENVVAR: container['name']}):
             # fire!
@@ -138,7 +162,7 @@ def __call__(cmd, container_name=None, dataset=None,
                     cmd=cmd,
                     dataset=dataset or (ds if ds.path == pwd else None),
                     inputs=inputs,
-                    extra_inputs=[image_path],
+                    extra_inputs=[image_path] + extra_inputs,
                     outputs=outputs,
                     message=message,
                     expand=expand,
diff --git a/datalad_container/tests/test_containers.py b/datalad_container/tests/test_containers.py
index 49ffca7c..16cb58dc 100644
--- a/datalad_container/tests/test_containers.py
+++ b/datalad_container/tests/test_containers.py
@@ -132,6 +132,46 @@ def test_container_files(ds_path=None, local_file=None, url=None):
     assert(not op.lexists(target_path))
 
 
+@with_tree(tree={
+    "container.img": "container",
+    "overlay1.img":  "overlay 1",
+    "overlay2.img":  "overlay 2",
+})
+def test_extra_inputs(ds_path=None):
+    container_file = 'container.img'
+    overlay1_file  = 'overlay1.img'
+    overlay2_file  = 'overlay2.img'
+
+    # prepare dataset:
+    ds = Dataset(ds_path).create(force=True)
+    ds.save()
+
+    ds.containers_add(
+        name="container",
+        image=container_file,
+        call_fmt="apptainer exec {img} {cmd}",
+    )
+    ds.containers_add(
+        name="container-with-overlay",
+        image=container_file,
+        call_fmt="apptainer exec --overlay {img_dirpath}/overlay1.img {img} {cmd}",
+        extra_input=[overlay1_file]
+    )
+    ds.containers_add(
+        name="container-with-two-overlays",
+        image=container_file,
+        call_fmt="apptainer exec --overlay {img_dirpath}/overlay1.img --overlay {img_dirpath}/overlay2.img:ro {img} {cmd}",
+        extra_input=[overlay1_file, overlay2_file]
+    )
+
+    res = ds.containers_list(**RAW_KWDS)
+    assert_result_count(res, 3)
+
+    assert_equal(ds.config.get("datalad.containers.container.extra-input"), None)
+    assert_equal(ds.config.get("datalad.containers.container-with-overlay.extra-input",get_all=True), "overlay1.img")
+    assert_equal(ds.config.get("datalad.containers.container-with-two-overlays.extra-input",get_all=True), ("overlay1.img", "overlay2.img"))
+
+
 @with_tempfile
 @with_tree(tree={'foo.img': "foo",
                  'bar.img': "bar"})
diff --git a/datalad_container/tests/test_run.py b/datalad_container/tests/test_run.py
index 184c96fd..4ff3248b 100644
--- a/datalad_container/tests/test_run.py
+++ b/datalad_container/tests/test_run.py
@@ -9,6 +9,7 @@
     containers_run,
     create,
 )
+from datalad.local.rerun import get_run_info
 from datalad.cmd import (
     StdOutCapture,
     WitlessRunner,
@@ -191,6 +192,47 @@ def test_custom_call_fmt(path=None, local_file=None):
     assert_in('image=../sub/righthere cmd=XXX img_dspath=../sub', out['stdout'])
 
 
+@with_tree(
+    tree={
+        "overlay1.img": "overlay1",
+        "sub": {
+            "containers": {"container.img": "image file"},
+            "overlays": {"overlay2.img": "overlay2", "overlay3.img": "overlay3"},
+        },
+    }
+)
+def test_extra_inputs(path=None):
+    ds = Dataset(path).create(force=True)
+    subds = ds.create("sub", force=True)
+    subds.containers_add(
+        "mycontainer",
+        image="containers/container.img",
+        call_fmt="echo image={img} cmd={cmd} img_dspath={img_dspath} img_dirpath={img_dirpath} > out.log",
+        extra_input=[
+            "overlay1.img",
+            "{img_dirpath}/../overlays/overlay2.img",
+            "{img_dspath}/overlays/overlay3.img",
+        ],
+    )
+    ds.save(recursive=True)  # record the entire tree of files etc
+    ds.containers_run("XXX", container_name="sub/mycontainer")
+    ok_file_has_content(
+        os.path.join(ds.repo.path, "out.log"),
+        "image=sub/containers/container.img",
+        re_=True,
+    )
+    commit_msg = ds.repo.call_git(["show", "--format=%B"])
+    cmd, runinfo = get_run_info(ds, commit_msg)
+    assert set(
+        [
+            "sub/containers/container.img",
+            "overlay1.img",
+            "sub/containers/../overlays/overlay2.img",
+            "sub/overlays/overlay3.img",
+        ]
+    ) == set(runinfo.get("extra_inputs", set()))
+
+
 @skip_if_no_network
 @with_tree(tree={"subdir": {"in": "innards"}})
 def test_run_no_explicit_dataset(path=None):
diff --git a/tools/ci/install-singularity.sh b/tools/ci/install-singularity.sh
index f031295c..430a9ce4 100755
--- a/tools/ci/install-singularity.sh
+++ b/tools/ci/install-singularity.sh
@@ -4,5 +4,7 @@ release="$(curl -fsSL https://api.github.com/repos/sylabs/singularity/releases/l
 codename="$(lsb_release -cs)"
 arch="$(dpkg --print-architecture)"
 wget -O /tmp/singularity-ce.deb https://github.com/sylabs/singularity/releases/download/$release/singularity-ce_${release#v}-${codename}_$arch.deb
+set -x
+sudo apt-get install uidmap
 sudo dpkg -i /tmp/singularity-ce.deb
 sudo apt-get install -f