Making the game more strategic..

The new building would be a "distribution center" where you could dump your excess men and it would distribute (like tax once a day) the men from it's defense to the nearest tile that has room. You will still need to capture new tiles, but for them to be filled and they have to be connected to the distribution center through your other tiles. So for example, the distribution center will not send men to the nearest tile, if that tile is not connected through other tiles you own. This will make war much more strategic than simply dumping your henchmen on random tiles with low defense. This will not make tiles invulnerable, as the regular tiles can be taken over with fill pockets since the distribution happens once a day, just like taxes do.
But it would make HQs more strategic resource, since taking over one HQs in a day is difficult, the best way would be by first cutting off the supply line from the "distribution center" and then laying siege.
And since this new building would distribute it's own defense, at the beginning of the each day it would be very weak with 0 defense (unless of course all connected tiles are full or the supply route to distant territories is broken). This would make it a prime target, before the siege and it's placement should be a very strategic place, like your place of residence for example.
To further offset it's value, it would be better to limit it's rebuild timer to about 1 month, unlike regular HQ at 1 week.

But it's value is not only strategic, from game-play. It would also stop people from leaving the game out of boredom, since once their nearby lands are filled they would have nothing else to do. And nobody in their sane mind would be driving for many miles around, several times a day just to empty 100 men and $10000 gold that accumulates 4several times a day. Not to mention from special missions. This would make the game more strategic and less about driving around, giving the HUGE advantage to those of us who can drive, or have jobs daily. While younger kids have nothing, and I'm sure no parent would waste gas driving kids around for no reason.
So many people get bored and leave the game because there's nothing else left to do, unless they want to leave their gang daily just to attack with the excess men their own territories and to re-join the same gang few minutes later. There's no point in gangs, when people have to leave all the time to just to continue playing the game. And what about those who are playing on their own? They cannot leave the game, nor do they want to give up their land just to be able to attack it once a day, after the nearby squares are full...