with no other qualification than what I've seen from the BA lounge at T3 I would guess there are 3 widebody stands on the BAMA side since there is often a BA and 2x AA 767s parked there at the same time. On the 'old domestic' side of T3 there are probably 2 wb stands so five altogether - so really it wouldn't work if BMI joined them fully (don't forget their domestic flights already use T3) .
I do feel sorry for MAPLC since they designed and funded this for BA on the basis of them operating 737 or equiv aircraft as they did at the time. Since BA have effectively 'lost it' at MAN they are literally a waste of space. A lot of top class infrastructure is cluttered up with Embraer jets and airbridges cannot be used and go to waste, and not to mention the waste of precious take off slots that BA take with half empty 50 seaters.
BA's business model is not and has never been suited to the Manchester market if you ask me - now evidenced by declining BA passenger numbers against a backdrop of increasing passenger numbers overall.