Assume your batteries are are presently two 12v 100 AH LFP with internal BMS's in series.
Not sure your descriptiion of connections but I believe you mean two separated serial strings versus strapping two 12v batteries together in parallel then putting the two parallel strapped batteries in series.
I generally do not like strapping cells directly in parallel. This needs matched cells which can only realistically be done by manufacturer. The fact that the additional batteries have not experienced the same usage and age is even more reason to maintain separate series combination of battery strings. BMS series resistance slight differences adds to the mismatching.
Be aware you will not likely get even current distribution between the two strings. You should get a clamp on DC amp meter to keep track of how the two strings are splitting the total charge or discharge current. Better then 20% current matching is considered good. Do not load them as if they are two times single battery for discharge or charging.
The fact you now have four independent BMS's create some complications. Any one of the four BMS's could open for whatever reason (overdischarge, too much current, overcharge on a cell, or temperature) so the safe way to run is to not discharge or charge any more current then could be handled by single string. You will still get near double the capacity having two strings in parallel.
Having at least a shunt and current monitor readout on each string would be a good idea so you can glance at current matching and know if a string went off line. I have ten strings in parallel, each with their own 100 amp shunt. This is in addition to a 500 amp shunt and full battery monitor on inverter main line. The more strings in parallel the better the odds most of the strings are in play so can raise the current charge and discharge to higher levels.
Another benefit of separate strings is you can pull one and still maintain inverter operation. I have my ten strings in five caster wheeled carts with Anderson SB350 connectors so I can easily pull a single cart out to work on.