Technically yes it would be doable to do it if thats what people decided they want.
if everyone over network accepts they want 2-3 millions coins more then would it be possible to generate/mine more coins?
If everyone agrees, anything can be changed in Bitcoin protocol without fork. But I doubt adding 2-3 millions coins is a thing everyone agrees with
How do you get everyone to agree though?
to get everyone to agree would be something like a bitcoin-QT version x.blah.. where each block suddenly rewards 50coins again and the reward halving is adjusted to make another 5mill coins dropping again. and thus everyone who upgrades their client is obviously in agreement that its what they want.
the opposing side where people do not want the new protocol would simply not download the update. and carry on using the old protocol. that is how bitcoin voting works. if you want protocol changes, download the update. if you dont, then stick with old versions of bitcoin. it may cause a fork and obviously the people with most users on whichever fork win. where value stays the same. and the least users find that they cannot transfer funds to the majority/exchanges/friends/and thus their fork becomes useless.
now from my point of view if bitcoin was to change the limit, the value would crumble to nothing, because once users realise that bitcoin is being flooded with another x amount of coins, the supply vs demand changes. and ontop of this the trust that value would hold/increase would disapear. and along with that people will start to think, if they can mess with the limit once. what is stopping them from doing it many times. and as such bitcoin would be useless as a store of value.
so there is no point in increasing the limit. it wont help anyone personally, and wont help the purpose of bitcoin.
