  Mixed superposition rules, i.e., functions describing the general solution of
a system of first-order differential equations in terms of a generic family of
particular solutions of first-order systems and some constants, are studied.
The main achievement is a generalization of the celebrated Lie-Scheffers
Theorem, characterizing systems admitting a mixed superposition rule. This
somehow unexpected result says that such systems are exactly Lie systems, i.e.,
they admit a standard superposition rule. This provides a new and powerful tool
for finding Lie systems, which is applied here to studying the Riccati
hierarchy and to retrieving some known results in a more efficient and simpler
way.
