Loved your post
. Many small neighbors instead of one large good neighbor on 3 sides gives us more bargaining power in bilateral matters.
But not now. Waging a war against India is suicidal, even with China and Pak on our side. Regardless of their "improving relation" with Pakistan or "good trade relations" with China, india's regional ambition is leading it to a head-on collision with both of them - maybe in 20, 50, 100, 500 or X number of years. There could be so many reasons for war (water sharing, territorial, natural resources in the oceans...).
BD Army can jump in and do it's job once india is worn out from a long war and signs ceasefire agreement with Pak+China (I don't see any other outcome, other than India and/or Pak losing some parts of their territories before signing the agreement). Believe me, india will have exhausted all their military power by then, fighting Pak-China with all they have. NE rebels aided by China will be fighting with new vigor. A few remaining 5th gen fighters and brahmos + whatever left will not act as much of a deterrence against BD Army.
We have to realize indian generals would take the "small annoying neighbor's" worst case scenario intentions into considerations while planning their military maneuvers, but they cannot afford to push BD into Chinese hands by launching an invasion against us. All our politicians need to do is stay warm towards india and be vocal about indian interests, at times.
Our generals and intelligence agencies (not our beloved politicians) must maintain this as a secret policy (encryption!) and maintain a fake friendship with india at all times till then. That is in our best interest!
Oh btw, don't mind the expected random barking by indian members - they are our brothers after all.