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Oh boy. This is a very subjective question. So fair warning: there is no way to know 100% for sure ahead of time unless one's ex challenges this and then the Court decides.
Alimony in Massachusetts may be modified if there is a "material change" in the financial circumstance of one of the parties that warrants the modification. Schuler v. Schuler, 416 NE 2d 197 - Mass: Supreme Judicial Court 1981. What material change means is on a case by case basis, but is generally defined to be a prolonged illness by one of the parties, an unsuspected loss of income, a big raise, inheritance, etc. Moving in with another person who shares the expenses also counts as this.
One's ex can attack this on two grounds. First, he can claim that the rental amount itself is "material change in circumstances" that should be applied towards the alimony being modified. Second, he can attempt to claim that the boyfriend is really moving in, but he is renting the room just as a "guise."
The Judge would be the one to make the final decision. However, I would be amiss to say that this would indeed give the ex some argument to modify alimony. Perhaps not to void it completely, but the Court may be critical of the new arrangement as something closing in on cohabitation, or simply enough itself to warrant a "material change."
However note, this is not automatic. The ex has to file in court and PROVE the above, which may not be easy.
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