I signed a guy to a max deal (during a rebuild) and thought about shopping him immediately. I was planning to start turning the corner that season, and thought the guy (huge bat, slightly below avg defense at 2B) might help me sneak into the playoffs. (this was also like my 3rd season playing HBD ever, so I was still learning - and farther from the playoffs than I thought). I was able to trade him (in year 2 of the deal, I think) for a couple good ML players, and learned some good lessons.
But... all that to say, I thought about shopping him since I had clearly been forced to go max by at least 1 owner who may have been willing to give me a stud prospect (or more) for him. In hindsight, I wish I had at least thrown it out there (but in the moment I was too geeked about having a player like that on my roster, especially after inheriting a bad team with little talent on the ML squad or on the farm).