  In high statistics observations of B^o --> J/\psi K0, originating from the
process Upsilon(4S)--> B0 B0, it should be possible to observe `cascade
mixing', where one mixing particle, the B0, turns into another, the K0. This is
possible despite the difficulty that the length of the beam crossing region
makes a precise definition of the primary vertex impossible. This difficulty is
circumvented by using an `away side' tag to specify the initial time. We review
the formalism for describing such processes, and first apply it to simple B0
mixing, noting it gives a transparent description for CP and T asymmetries. In
particular we show that three different asymmetries of the CP and T type, with
neglect of direct CP violation, are given by the same expression.
  For "cascade mixing" we present predictions for processes of the type B_i -->
K_j via J/psi, where in the limit of no direct CP violation each state i or j
is determined by a simple tag. There are 16 such simple measureable processes,
involving 10 functions of the two time intervals involved. The coefficients of
the functions are different for each of the processes and are given in terms of
the mass splitting and the CP, T violating parameter of the B0 mass matrix m_2.
The results presented here are just consquences of the quantum mechanics of
particle mixing and do not involve any particular model of CP violation.
