Three new transition metal borophosphates, CsCu(HO)[BPO(OH)] (denoted (I)), CsNi(HO)[BPO(OH)] (II) and mixed RbNiFe(HO)[BPO(OH)] (III), were synthesized by a boric acid flux method at 473-493 K. X-ray single-crystal diffraction study confirms their isotipy with (Cs/Rb)Co(HO)[BPO(OH)] borophosphates crystallizing in the orthorhombic space group Pbca. The crystal structures of all compounds are based on 3D frameworks made from corrugating borophosphate layers [BPO(OH)] and trimers of MO(HO) and two MO edge-sharing octahedra. The negative charge of the framework is compensated by alkali metal cations, Rb or Cs. Structural analysis reveals the flexibility of mixed anionic frameworks of the described structural type. The Cu-member demonstrates a strong distortion of the unit cell due to the Jahn-Teller effect of the d configuration of the Cu cation. The possibility of a solid solution between different transition metals (Fe and Ni) with the formation of crystals with mixed structural positions is confirmed by an example of the (III) phase. It is shown that Fe cations prefer to occupy the M2 position with more distorted oxygen environment, as compared to the M1O octahedra. Magnetic studies of (I), (II) and (III) prove that all compounds are paramagnets down to the lowest temperatures of measurements, 2 K. (I) and (II) compounds are thermally stable up to 500 °C. Different mechanisms of their thermal decomposition are discussed. The possibility of a wide isomorphous substitution at the transition metal sites of the title structure type opens the way to the modification of the properties in the discussed series of borophosphates.