05 Pre-runner bottoms out! Can't stand it!

I have an 05 Taco Pre-runner longbed with 20" rims currently running a moderate street tire. Everytime I tow a small utility trailer with some off-road toys it bottoms out everywhere. I thought about lifting the truck a little to put all terrain (a little more agressive) tires and increase my travel. I don't do off-road in the truck nor do want to create a monster truck of any kind. What would be the recommendation to accomplish a slightly larger tire (without rubbing when I turn) and stop the bottoming out. It is bone stock minus the rims and its a V-6. Any suggestions?

 

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