Please help in connecting the generator

Hello. I thought that you can help me solve one problem (if you can solve it, then, of course, not for free). I state in detail the essence of the problem:

At the present time, 380 V electricity (3 phases) is supplied to my country house. After the input panel, it is distributed throughout the house in single-phase 220 V wiring (there are no 380 consumers). Backup power is provided by the FUBAG BS6600 A ES. The generator has three power sockets (all 220 V, two 16A and one 32A), which are connected to the lines of each input phase. Before turning on the backup power, the main power line is cut off manually using automatic machines. Zero is also cut off, since single-phase generators do not have a full zero (there are two half-phases of 110V each). The generator has a connector for connecting an automation unit.

I have an automatic switching unit (in fact, an automation unit) FUBAG STARTMASTER BS 6600. It is single-phase. I checked its operation on the simulator of input power from the outlet, it works properly, starts the generator when the power is turned off (~ after 5 seconds), cuts off the input line when the generator is working, and turns off the generator when voltage appears on the input line of the main network and restores it back (~ through 15 seconds). In the automation unit, two contactors CJX2 2508 are installed.

Question: is it possible, when adding a certain number of contactors (how and where to install them I will find) to make the control carried out in three phases, and not one, as it is now? That is, so that if the voltage disappears at any of the input phases (or at one specific phase) of the input, the generator is started, the automation cuts off all three phases and zero of the input line and provides power in the house from three generator sockets.

If I stated something wrong, I stated (all the names are given exactly) in terms of electricity, sorry, I have basic knowledge. If I didn’t take into account something in the question, I can clarify it according to your instructions.

If the problem can be solved (installation, soldering, connection, continuity of circuits, measuring loads - all this I can do myself), please say how much the solution will cost. And what additional materials (I do not know what might be required, in my opinion, at least four more contactors are needed) are needed. If you can give the address, I will drop the photo and the picture with the connection of wires to the mail. If you yourself for some reason cannot solve the problem, can you tell me who can? Thank.