Nick Dear's play starts with Shakespeare on the stand, a witness at a trial for high treason. "What are your ties to the Earl of Southampton?" the judge's voice rings out. That, as they say, is the question.

The third Earl of Southampton, Henry Wriothesley, was at the heart of the Essex rebellion, a plot against Elizabeth I. Sentenced to death, but let off with life imprisonment, he's a key figure in the Stratford man's mystery. Shakespeare dedicated two narrative poems, Venus and Adonis and The Rape of Lucrece, to Wriothesley. "The love I dedicate to your lordship is without end," he wrote for the latter. "What I have done is yours; what I have to do is yours."

Was his patron, as some scholars suggest, also the "fair youth" of the Sonnets; their addressee one Mr W.H.? Or were the pair purely professional? There's no concrete evidence one way or the other. Those two dedications are all that remain.

Dear's play cycles through the possibilities. At once historical speculation and a critique of speculative history, Dedication – Shakespeare and Southampton imagines three versions of their relationship, channel hopping between parallel pasts. While Tom McKay's Shakespeare, thick-set and straightforward, stays constant, Tom Rhys Harries, gleaming in white, his hair bottle blond, is the golden boy of Southampton, and he changes in each.

One's flirtatious and haughty, a louche rich kid who picks up a poet. Another's imperious and stern, sought out by Shakespeare as a source of income – maybe more. The third is boyish and bright, a fey thinker and queer radical, prone to cross-dressing. This time, their appreciation – and attraction – is mutual. It's history as told by Goldilocks' three bears: too hot, too cold, just right. As well as the romance, Dedication picks at philanthropy: who works for who, poet or patron? Both men are masters here. One Southampton's demanding, another's awestruck. His money might dictate writing, or might just support it.

Any of these Southamptons would be capable of a coup, but, though Dear shows us three relationships, he doesn't show us three plots. Where Dedication draws nearest to known facts, the three Southamptons combine and Rhys Harries, deftly, nods to them all. The point, as Shakespeare states plainly, is that each version is simultaneously true and not true – a line of thinking Dear extends to homosexuality, rarely found in the record books, but no less a fact of life for that. He doesn't, however, apply the same notion to justice: as speculative and uncertain as history itself. Can we really know Wriothesley's role in the rebellion – or just that he was tried and convicted?

Too often Dear's writing tends towards aphorisms and factualities. At best, it's self-aware; at worst, unconvincing and glib. His Shakespeare never misses a chance to stress his Stratford connection or spell out the play's message. "It's a history play," he says of Richard II. "They're tricky." That's why Sam Hodges puts the pair on a pedestal. Alex Lowde's mirrored in-the-round stage encases them like Crown Jewels: two sparkling national treasures on show. Bissected by arches, it stresses our subjectivity; one's view of events depends on the angle of approach. Reflections bounce off each other, fragmenting the image. It underlines the two men's mutual vanity, but is itself vain: a moving catwalk, outlined in neon, its twin revolve spinning the pair past one another. It adds up, but subtracts: overloading a slight, concentrated play and distracting from it with wobbles, glitches and judders. History's full of them. Theatre probably shouldn't be.

Dedication runs at the Nuffield Theatre until 8 October.