Both times I applied (at VFS in London) in the last two years I had to write a letter to the High Commissioner of India to accompany my application saying that I would like a visa which allowed me to visit Nepal/Bhutan/Bangladesh (as appropriate) for a few days each. In both cases I had to invent some itinerary for my visits. In the one case they sent me over the road to a travel agents for an "official" itinerary -- bizarrely involving flights despite me being on a motorbike -- to supplement the application. A £10 scam.
When they grant you this your visa is stamped "RE-ENTRY FROM BANGLADESH, NEPAL, BHUTAN" (as appropriate). This "re-entry" allows you to side-step the two months nonsense.
In neither case were the dates for the other countries mentioned on the visa, it was a blanket re-entry allowance.
I was stymied in the first case because I put down a request to visit Nepal, Bhutan and Bangladesh but then they noticed I'd be coming from Pakistan which meant four entries into India which was, apparently, one too many. Go figure.