I want to "do the right thing" and re-buy a pc game maybe 3 more times, as I know for a fact I want to install it on 3 computers.

Is there a way I can keep my account and buy the game multiple times?

or am I stuck with making 3 accounts?

Thank you Kindly.

If these 3 computers are all yours then just install the game on all 3 computers. You don't need 3 accounts for this.

You could buy additional copies of the game as a gift and give them out to others. GOG still gets the money, and others get a free game. There isn't really a need though, as GOG doesn't limit the number of PCs you can install the game on.

You can buy gift keys like mistycoven mentioned as much as you like and not gift any of them if you like.
Gifting them would be fine of course but I think it'll contradict your "do the right thing" approach, since because in that case 3 gifted games are going to be installed on 6 computers or even more.

You can install on any computer you own and control ... as many instances as you like, all legally.

With GOG it is all about PC ownership not single game ownership. That's one of the major points of DRM-Free.

If you own 50 PCs you can legally install on everyone of them.
Of course, if any of those PCs do not reside in a premises you own, and you don't really have control of them, then you would be stretching the meaning of really own, no doubt past what is legal.

In the vein of u/foad01 and u/Timboli 's posts, if only one person will be playing the game at one time (assuming it's not like a free / freeware title, then who cares ;), especially if you will be the only person likely ever playing it, don't worry about it. Treat the game like a CD/DVD-based game of yore. If the above is accurate, don't feel the need to buy extra copies.

That said, I do encourage supporting GOG generally (and competition to Steam in general, mainly DRM-free), so you could buy more games for yourself or to give away. ;)

There's nothing stopping you from installing the game on as many computers as you want, (no tools exist for enforcement/checks) but you are licensed as a single user instance.

Do with that as you may.

Just want to add a print from the GOG website back when it had some sense of humour. Maybe still on terms and conditions, who knows.

Are these three computers your personal property? And do all three computers belong to your personal household?
Then you don't need to rebuy the game(s).
Simply install the same copy on all three computers. Of course you can keep your account...why wouldn't you?
As others have mentioned: simply buy the extra copies as gifts (nobody is keeping you from using the gift codes yourself).
But as I said above: if these computers are all yours and they all belong to your personal household - there is no need to spend that extra money. Nope - see above.

He could do that, but ultimately that wouldn't fix his issue - that's just buying a licence so someone else can use the game, not him (as gifting transfers the licence) He would need to hold on to the codes himself. This on the other hand is correct, provided the PCs are within his household - i.e. all his (they don't have to be in the same physical location)