This might be possible easily. You could try using a bunch of "Y-cables" to connect all of your fans to the various fan headers of the board.
Some background that might be boring:
Warning: Spoiler! (Click to show)
For 3-pin, the control works through changing the voltage that's put onto the second pin. It is 12 Volt for full speed of the fan. The board reduces the speed of a fan by supplying a reduced voltage. It is unclear what a board does exactly when you configure things in its BIOS menus, but you can guess a little. When you see a percentage setting and configure it, you can assume that it's simply a factor multiplied with that 12V voltage. This means if you set 0% speed, it means 0V and the fan stands still, gets zero power. If you set 40%, it means around 5V and the fans runs at some very reduced speed.
The 4-pin scheme is supposed to work differently. It is using a "PWM" signal on the fourth pin to control the speed and is always using a constant 12V on the second pin. If a fan header works like that, then 3-pin fans will always run at 100% speed on that fan header and you will not be able to control them.
Very often, the case fan headers on a motherboard will always do this "voltage control" second pin stuff to control fans, even if a fan header looks like it's 4-pin. They will never supply a correct PWM signal on the fourth pin. If this is the case for your motherboard (you should just try it), then you'll be able to control the speed of 3-pin fans even if connected to the board's 4-pin fan headers.
There might also be a setting to switch 4-pin fan headers of the motherboard between "voltage control" and "PWM control". This is often the case for the fan header intended for the CPU cooler.
You can connect multiple fans to a single fan header through using an "Y-cable". An Y-cable will wire everything needed to supply power to all connected fans. The speed signal that's sent back from one of the fans towards the motherboard will only be wired to a single fan. This means the speed you will see in BIOS screens or in software will be the speed of that particular fan. You can't know the speed of all of your connected fans.
When using Y-cables, you might want to look up power use in "A" = "Ampere" for the fans. From what I remember seeing somewhere, a fan header on a motherboard usually can supply 1A of power. If your fans each use 0.2A for example, you'll theoretically be able to connect a handful of them to a single fan header (I would be a bit scared).