I think, generally, motor proteins fulfill your conditions.
As they move back and forth (different conformations), they will be doing functions (moving things or different steps in the overall movement cycle), and to some degree maintain their active sites (binding sites?).
An example is the actin-myosin contraction cycle.
Another similar example could be proteins involved in membrane fusion during vesicle release in response to calcium ions entering a nerve terminal.
Go to SNARE protein and pore formation in this link.
This is a complex system with many parts binding other parts at different times during the process (which has a lot of other steps in addition).
Going the opposite way (from the membrane's point of view), clathrin is involved in vesicles pinching off from a membrane sheet. These molecules are flexible (implying a continuum of shapes) and bind to themselves and other proteins in order to form vesicles.
Another possible group could be enzymes moving along a linear molecule like DNA or RNA. I am guessing these are changing conformation as they cycle along, but I don't really know for sure.
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