Your living arrangements are unusual to say the least, a typical residential property has 1 working connection, occasionally a customer may require two ( one business one personal ) more that that is rare, I doubt all the people who share the property all use ‘BT’ as their provider, it’s Openreach that provide the lineplant anyway......the problem you will have , with no simple solution, is every time one of the occupants asks for a line, it’s probably assumed by whatever provider they chose, that an existing line is being taken over , so someone else’s service ceases and the new service starts in its place......it’s possible that if each applicant stressed to their provider that it’s a new line needed not a takeover , it may stop a working line being taken , but , if for example your street had a maximum of 20 connections ( 20 pairs at the DP ) and 15 of these were already in use with neighbours, then obviously if more than 5 lines needed someone isn’t going to have service.
There probably will be a physical limit to the property , the cable to your home may only be a 5 pair ( if underground) or a limit on how many dropwires can follow the same route from the pole to the house ( if overhead ) so even if there is capacity at the ‘DP’ , there isn’t capacity at the property.
There is a universal service obligation on Openreach, but it’s fair to say your property is already served, and no one guarantees the number of lines your property seems to need, if you need more you may have to arrange something akin to a business provide and pay more than a normal residential fee, that’s if you can get an order raised
