Is it possible to do some mods to a 13hp honda to gain more hp and if so how much hp could I gain?

nitrous and a watercooled supercharger should at least help you get on plane

afordablegokarts.com has stage 1 bolt on kits and a larger jet, heads, cams, roller rockers minkuni carbs etc............

oops its affordablegokarts.com

Go to a local kart racing shop. I race karts as one of my hobbies and some of these guys come out with these big honda motors that have so much horsepower that they cant keep the tires from spinning. Google kart engine builders or honda kart engines...ect and you might be able to find a builder near you. I have been told by these guys that once they start modding these engines they can get up into the 30 or 40 horse range but they have to rebuild them often. But these are heavily modded alchohol engines ... running around 9500 rpm. It would be worth checking into. On the small engines the best way to get the full hp is flow.