In Germany we have "Voting Districts" which all have the same amount of registered voters, They determine who get's into the Bundestag, There is one direct mandate and one federal mandate. Direct candidates can get in if they are elected by the majority of voters of their district. There are a few prominent examples of this happening.
The German system is a little complicated and perhaps bloated - our Bundestag is 600+ people and could lose a hundred or so without hurtung anyone - but the key issue is this one: Federal elections are federal and are counted at federal scale. State elections are counted at state level with representatives of each state forming the "Bundesrat", the counter-balance for the "Bundestag". That way there is a nice balance of power. Gridlock is less in Germany, because any party can join the fray (A party needs 5000 signatures to be able to found itself). That way we have coalitions and a good balance of power. At the same time Germany has a 5% hurdle parties need to take in order to be able to join the Bundestag, which prevents excess fragmentation and a chaos we had back in the Weimar Republik, pre-Third-Reich.
A good example for a flexible balance of power is the "big coalition" with Angela Merkel as Chancellor. Because the larger "Peoples Parties" SPD and CDU lost voters in the last 3 decades, they are forced to work together and keep an eye out for protest movements and Germanys equivalent of alternative conservatives such as the AFD. The Germany federation works surpsiingly well and also is quite stable.
All in all I think the Germany system has some very neat democratic mechanisms that the US should really try out.
My first order would be: Federal elections are federal, no intermediate 'state' level election.