Use a Button in one table to *add* to Lookup column in another table

I’m trying to add multiple people (who live a “People” table) to a mailing list (which lives in a “Mailing List” table) via a button (in that “People” table). The result should be that they’re added to a lookup column (in the “Mailing List” table).

Here’s my issue: I can add a single person via the button, but when I try to add the next person, it overrides the person I added previously. So basically I can only have a single person on the mailing list at a time.

My doc is below, and here’s my formula for the button:

ModifyRows(Filter([Mailing Lists], [List Name]=“List A”), [Mailing Lists].[People on List], Lookup(People, Name, thisRow.Name))

Would appreciate any help!