Can I replace the power supply and buy a bigger case for my Acer Veriton X2665G

Veriton X2665G maybe? I don't find a Veriton X2655G model.

Acer is having issues with some of their web portals this week, while almost everyone is on vacation. I can't bring up the service guide for it. It's a mid sized tower case though but IIRC they used somewhat of a custom motherboard and the smaller flex power supply on them. I should be able to look it up next week sometime if you remind me…

Sure, here's the motherboard layout:

It's an almost normal uATX form factor, but notice those ports loaded at the front (1-4)? Those are the ports for the front panel, and they aren't on wires like typical uATX MBs. That means that a different case will either require a lot of creative cabling or not bring the front ports out to use. The second big issue is the power supply. It uses an ATX12VO supply in a Flex form factor. Most third party cases expect an ATX sized supply instead, and most third party supplies don't match the 12VO spec.

The power supply used in these models is a smaller form factor than normal, to support the smaller case. Acer shipped them with two different sizes of PSUs (180W and 250W), depending on whether they had a discrete GPU or not. Here are the part numbers for them:

These are all 12VO supplies, so provide 12V power only to the motherboard, in two connectors, a 6 pin and a 4 pin. To put this motherboard in a different case you will likely have to also put a 12VO power supply in, since most third party cases use an ATX form factor instead of the Flex. 12VO power supplies are tough to find on the secondary market, but we can get you part numbers for Acer supplies that will fit third party cases.

Often it's easier to just go with a different new system that has the extra size and expansion capability than to mod these designs. They were really designed for the low end, small form factor market, not for expandability or gaming.