So even though there’s no examples of explicit dual church membership in the NT, there are some points where multiple fellowships interact that could be helpful in thinking through dual-church membership.
Paul’s partnership with the Philippians
In Phil 4 Paul says the Philippian church is in partnership with him as he does mission. They are part of their own fellowship, but they also express partnership with other churches.
We also see this this happen as the Gentile churches send financial support to the church in Jerusalem (Acts 11).
Paul’s fatherhood of the Corinthians
1Cor 4 Paul seems to say they the Corinthians Christians belong to him as well as their own leaders. “Even if you had ten thousand guardians in Christ, you do not have many fathers, for in Christ Jesus I became your father through the gospel.”.
This seem to suggest that Paul is more their leader than their existing leadership team (if there is any valid ones there at all). So it’s not that the Corinthians have two groups of leaders (they’re rebuked for that in ch1-3). Rather, Paul is claiming to have authority over them, above their leaders.
Against false teachers
Many times in the NT Christians are told to not belong to certain groups (Gal 2, Phil 3, 1John 2, etc.). So there’s an opportunity to belong to two groups, the church-group and the false-teaching group. But Christians are told to only belong to one. But this is on the basis of theological truth.
Next… Can leaders be held responsible for people who go to other churches? Should they?