Then there is the ‘Dual Level Voting’ name

That wikipedia enty has led me to Dualvoting.com, a site mainly in German but with the main page translated to English.

This site suggests the second choice of party vote. I suggests that the second choice might be dealt with by allowing voter to but an ‘x’ against their preferred party, and a ‘2’ against their second choice. Just a question of ballot design.

This site also points out that two choice voting is a form of two-round voting. It has the advantage over two rounds on different days, that people cannot change their mind between two rounds.

People are I think well used to the idea of second choices in many areas of life. They make it easy to give everyone a choice and be sure that everyone will get something they are happy enough with.

This idea of a second choice is also used for electing individuals, in a system called supplementary vote. It was used in the UK until recently for electing local authority mayors. It was changed to first past the post 2022. The change was justified because of a high level of invalid votes in one election (poor voting paper design?) and acccording to some because FPTP was thought to advantage the government party.