Successive possessive words

In the following phrase, should the word "interests" have an apostrophe?

We favor inter-agency collaboration in order to ensure that our clients’ interests’ triumph.

I have been unable to convince myself either way. Any guidance, especially in a formal academic sense, would be greatly appreciated.

Solution 1:

No apostrophe is needed. "Interests" is the subject of the verb "triumph".

We favor inter-agency collaboration in order to ensure that our clients’ interests triumph.

If, on the other hand, you wished to ensure the triumph (as a noun) of the interests of your clients, it could be possessive:

We favor inter-agency collaboration in order to ensure our clients’ interests’ triumph.