Multiple look-up fields in a many-to-many relationship

I have created a many-to-many relationship with Committee Members and Committee Meetings as parent tables. The child table is Meeting Engagement. I would like to be able select all committee members that attended a meeting in the Meeting Engagement table from the Committee Members table. I created a look-up field for committee member in the Committee Engagement table, and then duplicated it for all committee members. However, when I choose a different committee member, in a different field, all the other committee member look-up fields change to the one most recently selected. Is what I want to do possible?