Is it possible to hang a hammock beyond its stated length?

It won’t be too comfortable.but it is possible.

Add large link chain at both ends where the hooks are screwed into the trees.

Two things will happen:

1. If you hang the hammock tightly, as you will want to do so that it doesn’t sag into a too-uncomfortable parabola when you settle into it, then it will put a tremendous strain on the support lines. So if you use ropes, they’ll stretch – which will make the hammock sag eventually, anyway, or you’ll have to use chain, as suggested by @Tropical_Willie.

2. Because you’ll want the hammock to be strung somewhat tightly to lay with no more than a comfortable hammock-y sag when you use it, you’ll start with strong ropes or chains, pulled fairly tight to start with. That’s going to put a lot of strain on the trees. As @Tropical_Willie also says, you should be screwing an eye bolt or hook into the trees for the attachment points, because if you do as some do and wrap the chain or rope around the tree (which is, after all, an easier attachment), then you’ll girdle the tree and kill it. However you manage it, you’ll be putting a lot of strain on the trees.

Or you could just get a hammock stand.