Have a panpsychic reality, and the drug induces a shared consciousness.
If you decide to have panpsychism be a true feature of your universe, then you could use it as a ground to argue (or just handwave) for the plausibility of a conscious entity being put in such a state-of-mind that they end up picking up, sharing or leaking consciousness with their surroundings.
If your universal translation drug were instead a mind-altering drug that causes the user to receive or leak consciousness in this manner, then having two nearby sentient beings use the drug at the same time could allow them to communicate at a sort of shared-experience level, where the languages in which the thoughts are composed come packaged with their own interpretations.
Leaving it at this point would come with lots of corollaries, however, many of which could be showstoppers or add too much noise to your worldbuilding:
- It would be either impossible or a really cunning trick to lie to someone using the drug.
- Because of this, one couldmight be forced to take the drug as part of an interrogation in order to obtain information.
- There would probably be a thriving trade in using the drug to share experiences that are particularly valuable, or educational, or interesting, or...ahem...yes.
- You probably need to worldbuild a sensible picture of the "background noise" of conscious experience of everything else in their vicinity when they use the drug (all the way down to the fundamental wave/particles; all the way up to the lower hierarchies of their own brains?) and how they filter it out.
You could perhaps overcome some of these by designing around them, such as:
- Making users capable of "closing" their minds voluntarily while under the influence of the drug,
- Creating side effects which would render the drug unenjoyable to use as a form of recreation,
- Limiting the experiences being shared in some way (perhaps direct sensory is not shared, only "internal monologue"; perhaps you're limited to what the other entity is currently focusing on, etc.)
Could be fun. Could be too much. Hope it's helpful :)