Yes. Why? Because no one setup is perfect at everything, so whatever weaknesses the first rig has, your second rig should excel at. For example, if one rig is the most detailed rig you have, but is mediocre on prat, then your second rig should be the rig with the most prat.
And, as others have said, there's no shame in trying to come up with the one most well-rounded rig one can, neither.