With a K-1 with multi-state income, where do we go to adjust down-home state income (as some of that total is supposed to go to other states.

You Don't. home states tax residents on all their income. first, you need to determine if the income in the non-resident states is high enough where you have to file. Every state has different rules on what that threshold is.  then you would need to prepare returns for those nonresident states. these need to be prepared first. once the nonresident states are done and taxes computed you finish up your home state and take whatever credit your home state allows for taxes paid to the other states.