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Ricci-like solitons with arbitrary potential are introduced and studied onSasaki-like almost contact B-metric manifolds. It is proved that the Riccitensor of such a soliton is the vertical component of both B-metrics multipliedby a constant. It is established that gradient almost Ricci-like solitons haveconstant soliton coefficients. Explicit examples of Lie groups as manifolds ofdimensions 3 and 5 equipped with the structures studied are provided.

Ricci-like solitons with arbitrary potential and gradient almost Ricci-like solitons on Sasaki-like almost contact B-metric manifolds