Is anyone here a philosopher or economist working on the interpersonal comparison problem?

We can treat being indifferent between outcomes $p$ and $\neg p$ as implying utility (degree of desire) zero: $U\left(p\right)=U\left(\neg p\right)=0$. This is also a provable consequence of Jeffrey's utility theory where we assume that tautologies have utility zero. Then, insofar preferences can be observed (reports, choice behavior), we can compare the "sign" of desires. If you prefer outcome $q$ to outcome $p$, and $U\left(p\right)=0$, then $U\left(q\right)>0$. That is, you desire $q$ to a positive degree. Then we can compare desires between different people based on sign (positive, neutral, negative). This rules out utility functions being equivalent under addition of arbitrary constants. It is not the case that for arbitrary constants $b$, $U\ast =U+b$.

Moreover, humans are neurophysiologically similar to each other. Which makes it plausible that similar behavior indicates similar desires for different people. E.g. similar reactions to equal pain stimuli indicating similar aversion to pain, desire for drinking water after 24 hours without water being similar, etc. If we accept that some desires are likely similar for certain situations, we can use them for interpersonal comparisons. E.g. Alice desires $x$ as much as Bob, Alice desires $y$ two times as much as $x$, Bob desires $y$ four times much as $x$, so Bob desires $y$ two times as much as Alice. This rules out equivalence under multiplication with arbitrary positive constants $a$, i.e. it isn't the case that $U\ast =a\times U$.

The interpersonal comparison problem is similar to the problem of other minds: The fact that other people a structurally similar to us suggests, by inference to the best explanation, that they also have inner lives. The same line of reasoning makes it unlikely for there to be large differences (utility monsters) in desires with similar observable physiological correlates (behavior, brain activity).