When people talk about the "American rule," they usually mean a system where every party pays their own legal costs, and the winner is not compensated in any way for the costs of litigation. Using that as your basis, the American system itself is actually a "hybrid."
The details change a bit from jurisdiction to jurisdiction. But in general:
- The loser in many American civil cases is required to pay the actual court costs. These are not as substantial as the attorney's fees, but they can easily run into hundreds or thousands of dollars.
These costs are for things like filing fees, process servers, witness fees, court recorders and transcripts, and other costs that, generally speaking, are going to be the same no matter how much your lawyer charges. (Again, what specifically is included in costs depends on your jurisdiction). This imposes a non-trivial expense on the loser of a lawsuit, without allowing the other side to run up the costs to an outrageous figure by hiring huge teams of expensive lawyer, as is possible under the pure English system.
- While the "American rule" is the default rule in most or all American jurisdictions, there are generally rules that allow the Court to shift part or all of a prevailing party's legal fees to the other side under certain circumstances.
For example: in many courts, if you bring a frivolous motion, or a motion designed primarily to inflate the costs of the suit, the court can require you to immediately pay any attorneys' fees expended in responding to that motion, even if you eventually win the lawsuit as a whole. This is a more specific and targeted penalty for misconduct than the English rule.
Similarly, if the Court finds that the entire lawsuit you brought – or the defense you presented – was frivolous, or presented in bad faith, or under certain other circumstances, the Court can include attorney's fees in the final damage award, just as would have been done under the English rule.
The result is a hybrid system. The benefit of this hybrid system, at least in theory, is that frivolous lawsuits are discouraged, but lawsuits that have some merit – even if they are ultimately unsuccessful – do not have to worry about the imposition of massive costs. However, the disincentive is not as much as it might be, since the standards courts use to judge a motion or lawsuit "frivolous" are generally quite stringent.