Multiple arms, multiple cartridges and geometry?

I have read the debates regarding the benefits of different tonearm geometries......Lofgren A and B, Baerwald, Stevenson etc....and I appreciate the benefits of choosing where, on the vinyl record, one wishes to have the least spread of distortion.
I also have read where certain arms seem to perform better with one or other of these geometries?

I have two turntables with three different arms on each one and I have a total of over twenty five different cartridges.
Four of those arms have removable headshells and twenty of my cartridges are mounted on their own headshells ready for installation into any of those four tonearms.
How then.......can I have different geometries for each arm if I don't wish to re-align a cartridge within its headshell depending on the arm in which its installed?
Surely......I must select a single geometry for all my arms so that the cartridges fixed to their headshells....are truly interchangeable?