A need a brush that will airbrush with stamps for painting

Iv’e tried different settings with the jitter etc but the airbrush mode seems to move the image within the range of the brushes radius of falloff, not redirecting the whole range of the falloff onto different spots. The best I can do is to make a stamp image that is mostly space, with a very small image in the center.
Does this make sense? I essentially want to airbrush with an object (not a ‘blender object’) like a leaf or a rock at different sizes and rotations, which seems like the most obvious way to do this sort of task. Krita has this mode but I can’t find a name for this type of mode (‘stamp airbrush’?).
I love Krita but it can’t replace texture painting on the models themselves or general painting in-context.
(I would wet my pants if somebody told me that the Krita ‘engine’ was going to be available for integration into Blender. Hah, dream on.)