I usually have at least 6 teams a year.
And I never had any issues with rooting for other players, even Eagles players, because I don't do any rooting.
I draft the players I want, whoever they are, set my rosters based on who I think will have a good game, and then I forget about it over the weekend. I don't look at the results until Monday night. This way I'm not, for example, watching the Giants and Cowboys knowing that Manning, who is on one of my teams, needs X amount of points for my team to win.