In a "First past the post" electoral system, It's always more advantageous for the 3rd party to merge with the first or second party.

New Zealand changed away from First Past the Post to Mixed Member Proportional in order to fix that

https://en.wikipedia.org/wiki/Mixed-member_proportional_repr...

https://en.wikipedia.org/wiki/Electoral_system_of_New_Zealan...

I'm not sure how you'd implement it, particularly at the senate level.