Don't plug the Puritan into the Furman. First, the Puritan is better than the Furman (I own a Furman Elite-15 PFi and a 156). Second, cascading power conditioners like that is very likely to rob your music of dynamics, especially the amplifiers with no real positives that I can see. An affordable tweak that is talked about in other threads on here are the Vera-Fi Snubway and MainStream plug ins. I think they make an audible difference and they have a 30 day return policy.
Puritan 156 and Furman
I am currently using a Puritan 156, and was thinking of putting my Furman back into the mix, I know I have to try it so I won't ask if it will improve anything. So I would plug the Puritan into the Furman.
My question is any possible negatives doing this? Here is the unit I have.