I need to click on an object that can exist multiple times on a web page.

you can use FindAllChildren from the parent object to get all

Similar

objects.
you may use common property and value for all the objects you are looking for.

once you have array of objects can operate click on each using index of array.

I'm not sure how far that could be achieved in keyword test...I'm doing only scripting
if not possible just write a small script and call it from keyword.
you can take idea and modify code shown here