Alice is hovering over the send button, about to come out to her parents, when her long-term partner Fiona comes out to her. She is – or rather he is – a man in a woman's body, eager to press ahead with the process of transitioning, first living as a man, then onto hormone therapy and perhaps even surgery. Alice has only just accepted her sexuality and now she's dating an Adrian.

Transferring into town from Theatre503, Jon Brittain's light-hearted look at the trans-experience is an amiable, if superficial, thing. Sitcoms thrive on identity crises and Rotterdam's chock full of them. In a port city that people pass through, the old year knocking into the new, Adrian isn't the only one in transition.

Rotterdam has long been Alice's limbo. She arrived, for work, in a relationship with dorky Josh (Ed Eales-White) and ended up seeing his sister and staying on seven years. As her relationship falters, she strikes a flirtatious friendship with Lelani (Jessica Clarke), a stock Eurochick who's open to everything, and discovers a whole new side to herself. New Year, new you – all round.

Identity isn't a fixed thing. It's fluid and forged in relation to others. If Alice identifies as a lesbian, what does it mean for her partner to identify as male? As Anna Martine's Adrian hardens into his real self, so sure of his identity even if others aren't, Alice falls further and further into flux. At the same time, though she's finding herself – a neat counterweight – growing confident, carefree and impulsive under Lelani's influence. By hanging on to the past, meanwhile, Josh shows the dangers of defining one's self by other people.

Brittain takes a sitcom tone, one that makes a hefty issue immediately accessible, at the cost of complexity and credibility. Really, Rotterdam's a beginner's guide to the trans experience – a transplainer – but the script can feel more like a public infomerical than decent drama. It's all superficial and over-simplification. Characters speak for our benefit more than their own. "What's the word for when your body and gender match up?" Josh asks. "Cis," we're helpfully informed. It's not that Rotterdam isn't truthful – and its heart is in the right place – rather that its truth is too tidy and pat.

There are good reasons for setting things simply, and Brittain lays out the process, politics and perceptions of transitioning, but it comes at the expense of good drama. Donnacadh O'Briain's staging aims for all-out larkiness, so that everything insists theatre's fun, fun, fun. Keegan Curran's soundtrack drops club anthems – some, like Robyn's "Dancing on My Own", teeth-grindingly literal – into the scene changes, and Ellan Parry's design splashes bold block colours over a Rotterdam backdrop.

Yet, a committed, sparky and engaging cast keep it watchable, carving out characters you care for, despite disbelieving. Alice McCarthy brings a dry humour to the indecisive Alice, making her uncertainty both universal and infuriating, while Martine carefully calibrates the route from Fiona to Adrian and Jessica Clark makes you fall for Lelani – an entrancing mix of alpha assurance and manic pixie dream girl dolled up like a discoball.

Rotterdam runs at Trafalgar Studios until 27 August.