How to snap vertices to inclined plane?

Is there a way to snap vertices to an inclined plane? If I set snap to face it wants to snap on the face, but does not respect my G Z axis lock. It wants to snap on the face but near the cursor.

Blend file:
snap to face.blend (105 KB)

Yea, that’s a limitation of the snapping system. It can’t snap to cross-section of axis constraint and the target. But you can still do it with this

Since this is moving along Z, I’m snapping vertices from the top view on a face. I enabled face snapping, toggled off snap to itself and turned on snap to other objects (arrows). It doesn’t respect the axis lock in user perspective so it’s more like projecting vertices from a view.

Your objects have unapplied rotation in case that causes problems at some point.

I had tried to do that but I must not have had the project button toggled. Works great. From top view G Z then enter and it drops the selected vertices to the plane.

Thanks @JA12

Shrinkwrap modifier -Project and vertex group does it too.