Expand interference check tool frames (UT-Hand Definitions)

I wish to expand the number of tool frames that it allows assignments for under the interference check UT-Definition.
I opened up my tool frames to allow for my 23 TCPs (4 different physical tools) but I do not have that many under the UT-Definition which only has 14.
Does anyone know the System Variable that I can change to allow for the extra tool frames?
Thanks!