There are only two options for you: Replace the motherboard, or use a USB hub.
Replacing the motherboard would be major surgery. If you don't know exactly what you are doing, you can damage it in the process.
A USB hub, on the other hand, simply plugs in and gives you more USB ports. In your case, it would be more USB2 ports, because your USB3 ports are on the bad side of the computer.
If you decide to go with a USB hub, make sure you get one which has its own power, that is, one which has an AC adapter. Sometimes devices won't be able to draw sufficient power when plugged into a hub, unless that hub has its own power.