The problem with connect most fans to the PSU is that they won't be temperature controlled, they'll just spin at full speed all the time.
For this reason you might want to have a look at some fan controllers, some of these will let you connect multiple 3-pin fans using a molex connector which makes hooking them up a bit easier, and let you either control the speed manually with controls that go on the front of your computer (usually with a 5.25" front plate) or you can get some that include temperature probes so you can set a target temperature for the fans to base their speed upon.
How many fans do you actually have in total though, and in what arrangement? IMO two motherboard fan connectors is usually enough for connecting two big fans, one at the front of a case and one at the back (including big dual fans if you can fit them), as quantity of fans isn't as important as getting strong steady airflow, and usually limiting it to one direction works best. I'd only recommend using more individual fan units if your case is separated into sections (or you've done that yourself) since those can operate independently.
Also, depending upon the fans you're using and the components in the case sometimes all you need are exhaust fans at the back as they'll pull air in at the front anyway, though the front fan working in tandem can help if that's not enough.