  We discuss how a q-mutation relation can be deformed replacing a pair of
conjugate operators with two other and unrelated operators, as it is done in
the construction of pseudo-fermions, pseudo-bosons and truncated pseudo-bosons.
This deformation involves interesting mathematical problems and suggests
possible applications to pseudo-hermitian quantum mechanics. We construct
bi-coherent states associated to $\D$-pseudo-quons, and we show that they share
many of their properties with ordinary coherent states. In particular, we find
conditions for these states to exist, to be eigenstates of suitable
annihilation operators and to give rise to a resolution of the identity. Two
examples are discussed in details, one connected to an unbounded similarity
map, and the other to a bounded map.
