  Ricci-like solitons with arbitrary potential are introduced and studied on
Sasaki-like almost contact B-metric manifolds. It is proved that the Ricci
tensor of such a soliton is the vertical component of both B-metrics multiplied
by a constant. It is established that gradient almost Ricci-like solitons have
constant soliton coefficients. Explicit examples of Lie groups as manifolds of
dimensions 3 and 5 equipped with the structures studied are provided.
