It is a commonplace, indeed, that many happy marriages admit a party of the third part.
By the way, does the paper say who the party of the second part was?
Happy am I to report that this silly agreement was kept by the party of the first part and Michael.
There was no time to continue the discussion before the parties of the second part returned to face their accusers.
That the party of the second part shall quietly enjoy the said premises.
"Do you suppose the party of the first part is completely unaware of these things?"
I've never seen one quite like this, if that's what the party of the first part has in mind.
It remained a "dead secret" between the parties of the first and second part forever.
You might say it's the party of the second part.
It can also be dangerous unless the party of the second part understands.