Arrangement comprising a turbomachine inner housing, for a radial turbomachine, wherein the turbomachine inner housing has a dividing line along a longitudinal axis, in particular a rotor longitudinal axis, such that the turbomachine inner housing can be divided into a lower part and an upper part, wherein the turbomachine inner housing is designed for a radial turbomachine comprising at least two stages, wherein the turbomachine inner housing has a return stage between each two stages, wherein the return stage is designed in such a way, that within the turbomachine inner housing in the downstream section of the annular channel of the return stage, the process fluid is deflected by 180° radially inwards and then guided further radially inwards through a guide-bladed section, whereby a 90° deflection in the downstream axial direction to the next upstream impeller takes place, the lower part and/or the upper part are/is formed in one piece, spanning at least two stages at least in some sections, wherein the turbomachine inner housing has at least two return stages, wherein the turbomachine inner housing has an inner surface defining the inside of the turbomachine inner housing and an outer surface, wherein the outer surface has at least one recess extending radially inwards axially between two return stages, wherein the arrangement furthermore comprises a turbomachine outer housing surrounding the turbomachine inner housing, wherein the arrangement has an axial low pressure side and an axial high pressure side, wherein the arrangement has a seal, which extends in the circumferential direction and is arranged in a space between the high pressure side and the low pressure side in such a manner that the space is divided into a high pressure part and a low pressure part, wherein the high-pressure part is operating under a final pressure of the turbomachine, and the low-pressure part is operating under an intake pressure, wherein the recesses are in each case arranged between the at least two adjacent return stages and in the region of the high-pressure part, wherein the turbomachine inner housing consists of up to 50% by weight of metal and at least 50% by weight of plastic. wherein the turbomachine inner housing has a dividing line along a longitudinal axis, in particular a rotor longitudinal axis, such that the turbomachine inner housing can be divided into a lower part and an upper part, wherein the turbomachine inner housing is designed for a radial turbomachine comprising at least two stages, wherein the turbomachine inner housing has a return stage between each two stages, wherein the return stage is designed in such a way, that within the turbomachine inner housing in the downstream section of the annular channel of the return stage, the process fluid is deflected by 180° radially inwards and then guided further radially inwards through a guide-bladed section, whereby a 90° deflection in the downstream axial direction to the next upstream impeller takes place, the lower part and/or the upper part are/is formed in one piece, spanning at least two stages at least in some sections, wherein the turbomachine inner housing has at least two return stages, wherein the turbomachine inner housing has an inner surface defining the inside of the turbomachine inner housing and an outer surface, wherein the outer surface has at least one recess extending radially inwards axially between two return stages, wherein the arrangement furthermore comprises a turbomachine outer housing surrounding the turbomachine inner housing, wherein the arrangement has an axial low pressure side and an axial high pressure side, wherein the arrangement has a seal, which extends in the circumferential direction and is arranged in a space between the high pressure side and the low pressure side in such a manner that the space is divided into a high pressure part and a low pressure part, wherein the high-pressure part is operating under a final pressure of the turbomachine, and the low-pressure part is operating under an intake pressure, wherein the recesses are in each case arranged between the at least two adjacent return stages and in the region of the high-pressure part, wherein the turbomachine inner housing consists of up to 50% by weight of metal and at least 50% by weight of plastic.