When developing with Pyrocat-HD I do not recommend pouring the exhausted developer back into the tank after fixing, nor do I recommend any kind of post-development alkaline bath. Any additional stain that may result from this kind of treatment is mostly general stain, or b+f, and does nothing to enhance the printing qualities of the negative.
My post-development procedure is:
1) Stop bath, in water with several complete changes, or in an acetic acid stop bath diluted to about 1/2 normal strength.
2) Fix in an alkaline fixer such as TF3 or TF4 for 4-5 minutes.
3) Wash for 15-20 minutes in running water.