Is there a reasonable way to work with multiple AC units in the same space?

My wife and I recently bought a house. We are actually pretty cold climate people but are aware that we have to adjust. Since we bought the house in the winter, we were a bit unsure as to how well the air conditioner worked. Recently the temperature has gotten up into the high eighties and I noticed that our air conditioner was on constantly to keep the house at 76F. Actually, it wasn’t even very successfull at that, so I called an AC repairman to check it out. Actually, he took one look at the unit and said “This is for the entire house?” Apparently the previous owners were extremely hot weather people, because our AC unit is working splendidly. This unit just isn’t rated for a house as large as ours. For five thousand bucks he was happy to get a second unit installed, but that is not in our budget.

Now ordinarily, I would insist on sweating it out. As it happens though, I am going to be a daddy in a few days, and I am a little concerned as to how a newborn will take the heat that is undoubtedly coming. Even if the newborne is fine, my wife that will have to get up every two hours to breastfeed this new satan spawn will be very unhappy. At first, my suggestion was to get a little window unit just for the bedroom. Then I went to Walmart to check things out and I saw a nice 17000 BTU that was meant for about 1200 sqft and I thought, “Why that would be enough for the entire first floor!” Heck, if I threw in a cheapy window unit for the bedroom, we should be pretty comfy this summer.

Already though, I saw a problem. If I had three different air conditioners effectively cooling the same space, then I’m pretty sure one air conditioner would be pulling most of the weight while the others just kicked in on occasion for support. well it may not work exactly like that, but it is thew best way I can explain what I think the problem might be.

Unfortunately, when I went back to review the options i came to realize that the monster window AC unit that I had though would cool the entire first floor actually requires a 220V outlet. I only have one of those that I know of, and besides being nowhere near a window, it is occupied by the dryer. So then I am left with the option of having several AC units on the first floor. While with one AC unit in the bedroom and another on the first floor I might not be terribly concerned about the distribution of power, multiple units on one floor starts to confuse me.

So what I am really asking is, “Can I get all of these air conditioners to work in harmony?”

i saw on “ask this old house” that there is a unit that straddles the window unit-central air divide.

it has the usual inside bit of the window unit, but the noisy bit that goes ka-boom-chinga- chinga, etc. is on the outside. the nifty thing is that you can hook up 4 of the inside bits to the one outside bit. of course i can’t remember the name of this nifty thing.

hopefully someone will be by with the name of the nifty new hybrid thing.