... whether it is theoretically possible for a speaker driver to have greater IMD than its THD chart would suggest.
A simple example: a bass has hardly any distortion deep down, no distortion further up. There is such a thing. But now, with a longer excursion, the shape of the suspension changes, possibly even resonantly. And thus the amplitude of a medium tone. This means that the excursion by the low tone modulates the amplitude of the higher tone: AM aka IM Without harmonic distortions in the two frequency ranges being relevant in themselves.
Whitebox testing would focus on the resonance of the suspension, and test the deformation by simultaneously reproducing bass. Sometimes the IM is acceptable, sometimes not. The popular nasty multitone story hardly reveals an effect, because the disturbance barely gets above the background noise. But with a thinned out signal the case becomes immediately noticeable. Also for the hearing.
The by now well known bass driver SB Acoustics 17NAC of Revel / Burchardt fame shows this behaviour of course, too, but very well damped. Another one at 6 times the price has chosen a way less damped "lowest loss" suspension, which keeps the HD part extremely low, but the generated IM spreads over a remarkably wide frequency range once the right tones are hit, and thus becomes disturbing.
As already mentioned, without any HD indications.
With very small, almost extremely small loudspeakers like here (IL-10), you can always expect occasional overload at HIFI-compatible volumes. Whether the spectrum of disturbances is limited or reaches far up depends on the construction. In general this is not tested at all, because you would have to take components up to H10 or so with you. IM components can also scatter very widely. I speculate that these, together with the strong resonances of hard diaphragms that are common today, contribute to an individual sound that eventually becomes noticeable. (You cannot remove this with an XO, because the generator is the motor/suspension, not the input!)) And from then on you always have it in your ears... just a speculation.
Really low-resonance loudspeakers are boring - all experts like to say that - but they seem to me to be more pleasant in the long run.
Finally an anecdote (again): a highly respected PA midrange driver, low HD, flat amplitude response, only humble ondulations up high, that famous one with the flat suspension failed, according to my criteria, miserably. The bandwith was already limited digitally to a quite narrow 400Hz to 1,5kHz or so, but the - aurally quite disruptive - IM went up to 10kHz. Even higher than the raw frequency response of the driver! What a beast of a kinky sound signature! But some people still swear on it.