Mixed-member proportional representation provides for geographic districts, while still ensuring that every party gets no more seats than its popular vote percentage.
You can hardly do MMP in America. Several states have only one or two seats, where MMP would be equivalent to FPTP or block vote - a significant step back.
You'd need to do it on the national level, not state. Our parties transcend state boundaries anyway, and House was always supposed to be representing people as a whole; the states have the Senate for their representation as entities.
I dunno, I'm just trying to play with the rules that exist. There's a dubious federal law designed to ensure minority representation which seems to prohibit proportional representation, but seeing as it so abjectly fails to achieve its goals it may have no grounds to stand on. A state which thought democracy was a good idea and might be useful trying in the US[] could unilaterally introduce a bill and it may succeed in the courts. But it's unthinkable that you could get enough states to pass an amendment to the constitution to abolish state-based districts without an experiment in proportional voting in the US first.
[]: I don't mean to say FPTP is undemocratic - Canada is plainly democratic - just that America isn't democratic in much the same way one says Russia isn't democratic. If the government is intent on not hearing the will of the people, it will find a way.