If I understand correctly, number of targeted profile attribute and experiences mapped to them are too many, and that is why you are not comfortable driving these variations with dedicated audience.
If you are not building dedicated audience, you can create single qualifying audience and put the variation logic in the modal code itself. Bunch of IF ELSE blocks.
But this will turn out to be a nightmare for you from a manageability standpoint.
Second Option is to externalize the Modal Functionality as a remote offer. You can wire the single audience to a remote offer service, passing the attribute to it and service evaluates the attribute an return the right modal expereince.
Again still a bad idea, coz then I am not sure why you are using Target.
Depending on what your priorities are, multiple audiences mapped to each variation of modal on Target, is your best bet.