diff --git a/unyt/_array_functions.py b/unyt/_array_functions.py
index 6b321aca..06232e47 100644
--- a/unyt/_array_functions.py
+++ b/unyt/_array_functions.py
@@ -13,6 +13,32 @@
     UnytError,
 )
 
+# Functions for which passing units doesn't make sense
+# bail out with NotImplemented (escalated to TypeError by numpy)
+_UNSUPPORTED_FUNCTIONS = {
+    # Polynomials
+    np.poly,
+    np.polyadd,
+    np.polyder,
+    np.polydiv,
+    np.polyfit,
+    np.polyint,
+    np.polymul,
+    np.polysub,
+    np.polyval,
+    np.roots,
+    np.vander,
+    # datetime64 is not a sensible dtype for unyt_array
+    np.datetime_as_string,
+    np.busday_count,
+    np.busday_offset,
+    np.is_busday,
+    # not clear how to approach
+    np.piecewise,  # astropy.units doens't have a simple implementation either
+    np.packbits,
+    np.unpackbits,
+}
+
 _HANDLED_FUNCTIONS = {}
 
 
diff --git a/unyt/array.py b/unyt/array.py
index 98645689..71c5b69c 100644
--- a/unyt/array.py
+++ b/unyt/array.py
@@ -1982,7 +1982,13 @@ def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
     def __array_function__(self, func, types, args, kwargs):
         # Follow NEP 18 guidelines
         # https://numpy.org/neps/nep-0018-array-function-protocol.html
-        from unyt._array_functions import _HANDLED_FUNCTIONS
+        from unyt._array_functions import _HANDLED_FUNCTIONS, _UNSUPPORTED_FUNCTIONS
+
+        if func in _UNSUPPORTED_FUNCTIONS:
+            # following NEP 18, return NotImplemented as a sentinel value
+            # which will lead to raising a TypeError, while
+            # leaving other arguments a chance to take the lead
+            return NotImplemented
 
         if func not in _HANDLED_FUNCTIONS:
             # default to numpy's private implementation
diff --git a/unyt/tests/test_array_functions.py b/unyt/tests/test_array_functions.py
index d5f5f3b9..b75e6a0b 100644
--- a/unyt/tests/test_array_functions.py
+++ b/unyt/tests/test_array_functions.py
@@ -7,7 +7,10 @@
 from packaging.version import Version
 
 from unyt import A, K, cm, degC, degF, delta_degC, g, km, rad, s
-from unyt._array_functions import _HANDLED_FUNCTIONS as HANDLED_FUNCTIONS
+from unyt._array_functions import (
+    _HANDLED_FUNCTIONS as HANDLED_FUNCTIONS,
+    _UNSUPPORTED_FUNCTIONS as UNSUPPORTED_FUNCTIONS,
+)
 from unyt.array import unyt_array, unyt_quantity
 from unyt.exceptions import (
     InvalidUnitOperation,
@@ -150,36 +153,16 @@
     np.take_along_axis,  # works out of the box (tested)
 }
 
-# Functions that are wrappable but don't really make sense with units
+# Functions for which behaviour is intentionally left to default
 IGNORED_FUNCTIONS = {
-    # Polynomials
-    np.poly,
-    np.polyadd,
-    np.polyder,
-    np.polydiv,
-    np.polyfit,
-    np.polyint,
-    np.polymul,
-    np.polysub,
-    np.polyval,
-    np.roots,
-    np.vander,
+    np.i0,
     # IO functions (no way to add units)
     np.save,
     np.savez,
     np.savez_compressed,
-    # datetime64 is not a sensible dtype for unyt_array
-    np.datetime_as_string,
-    np.busday_count,
-    np.busday_offset,
-    np.is_busday,
-    # not clear how to approach
-    np.piecewise,  # astropy.units doens't have a simple implementation either
-    np.packbits,
-    np.unpackbits,
-    np.i0,
 }
 
+
 # this set represents all functions that need inspection, tests, or both
 # it is always possible that some of its elements belong in NOOP_FUNCTIONS
 TODO_FUNCTIONS = {
@@ -206,7 +189,9 @@
     "cumproduct",  # deprecated in numpy 1.25
 }
 
-NOT_HANDLED_FUNCTIONS = NOOP_FUNCTIONS | TODO_FUNCTIONS | IGNORED_FUNCTIONS
+NOT_HANDLED_FUNCTIONS = (
+    NOOP_FUNCTIONS | TODO_FUNCTIONS | UNSUPPORTED_FUNCTIONS | IGNORED_FUNCTIONS
+)
 
 for func in DEPRECATED_FUNCTIONS:
     if hasattr(np, func):