We place this construction into a unified framework of (n − t)-fold character theories ap- plicable to any ∞-commutative monoid. Concretely, for an ∞-commutative monoid R there is a universal (n − t)-fold character map that respects the natural induction and restriction structures of R. In particular, it yields a character theory for every T(n)-local algebra. This universal character enjoys strong structural properties: it exhibits a blue-shift phenomenon by sending T(n)-local algebras to T(t)-local algebras, and it carries primitive height-n roots of unity to primitive height-t roots of unity. In the case of En, it recovers the classical transchro- matic character.