Having a homomorphic encryption scheme like BGV or LTV-FHE at some point it is possible in the homomorphic evaluation to deal with ciphertexts that are encrypted with respect to different moduli.
For the chosen scheme we have a ladder of decreasing moduli $q_0 > ... > q_{t-1}$. If there is a ciphertext $c_1$ w.r.t $R_{q_2}$ and another ciphertext $c_2$ w.r.t to $R_{q_4}$, the first ciphertext should be "switched" into the ring $R_{q_4}$ and only then the homomorphic computation could be done ?
Or maybe this situation should be avoided ? Then, if this is the case, how about computation represented as an unbalanced tree of multiplications? At some point there will be a need to multiply two ciphertexts encrypted in different subrings.