Did you hear the one about the comedian who was as good at avant-garde theatre as he was at cracking gags?

The "thing" about comedian Daniel Kitson has always been the belligerent modus operandi – no interviews, no agent or manager, no press releases, no TV work … just word-of-mouth, a mailing list policed by Kitson himself, and a shedload of glowing reviews. The result being huge success and little or no public profile.

But there's plenty more to consider about the reclusive 36-year-old, such as his carving out of two parallel careers: one in comedy, one in theatre. Like those wartime sportsmen – say, Denis Compton – who would summer on the cricket pitch and winter on the football field, Kitson moves between standup shows and theatrical productions – a natural linguistic athlete who can't be contained to just one discipline.

This isn't just a case of a comedian dabbling in acting, but a comedian writing, directing and starring in one-man plays. It must be galling for other comedians to see someone nail their chosen artform, then cross over into another with such success – Kitson's 2010 show It's Always Right Now, Until It's Later crashed the National Theatre website when tickets went on sale, and the critical acclaim has barely stopped since he won the Scotsman Fringe First award in 2005 for Stories for the Wobbly-Hearted.

Constrained by standup? Daniel Kitson. Photograph: Dan Sparham/Rex Features

However, the further Kitson gets into his career, the more that straight standup seems unable to scratch all of his itches. He is an artist, ultimately, restless and ambitious, and standup is a constrained form. Theatre allows him room to experiment, as he did with his multi-layered 2012 monologue As of 1:52 GMT on Friday April 27th 2012, This Show Has No Title. And there's no more experimental show of his than his new one, Analog.Ue.

In it, the stage is in near-darkness and Kitson says not one word, but operates 46 tape decks in order to tell a pre-recorded story. We are, at this point, quite some distance from standup comedy. For me it's his least enjoyable show to date, an indulgence too far, where the story suffers at the hands of the concept. But the impulse behind it – to abandon the comfort zone and just try something – will surely bear fruit.

His increasing shift towards theatre has been quite useful for anyone who has attempted to compare him to others, as there aren't really other comedians who are similar. Now, however, you can reach for Samuel Beckett. Broadly speaking there's an uncompromising bloody-mindedness to Kitson that is quite Beckettian, whether it's his absolute control over his output, or the obsessive technical rigour that's required of Analog.Ue. (Geometrics and mathematics were key aspects of Beckett's methods.) Both are also drawn towards the metaphysical and the minuscule, rarely anything in between. Most overtly, two of Kitson's theatre shows – Tree (2013) and Analog.Ue – strongly resemble Waiting for Godot and Krapp's Last Tape respectively, in their set-up.

It says something about Kitson's development as a theatremaker that he is wearing this particular influence quite heavily, aping Beckett rather than fully embracing him.

Staging is one thing, words are another, and Alan Bennett is now another touchstone for Kitson comparisons, due to his home-spun pithy northern wit, though that neglects the density of Kitson's language, and his penchant for ironic locker-room banter. And the swearing. Of course, it's Kitson's formidable writing that brings the laughter, so it's not unusual for his theatrical monologues to be packed with gags as well. However far he decides to major on theatre, as a comedian the impulse to make a room of strangers laugh is in his blood.

Meanwhile, Kitson's standup shows have, on the face of it, been kept pure and free from theatrical flourishes, that is until his 2013 show After the Beginning Before the End, which came complete with a soundtrack manipulated onstage by a distinctly sat-down Kitson. But he has always been a theatrical standup.

How many comedians seem interested in moving their audience – a distinctly theatrical imperative? Virtually none, because that would require sincerity, which is the death of comedy. But it's part of Kitson's appeal that even his comedy shows have emotional resonance, going right back to It's the Fireworks Talking (2007) and his Perrier award-winning show Something (2002).

Kitson, who did a drama degree prior to his standup career, takes a sort of director's commentary role via the tape decks in Analog.Ue and expresses frustration and dissatisfaction at the life he's built around him. He sounds like a man in search of a clean slate, or a way out, as if neither comedy nor theatre are bringing him much joy. What happens next is anyone's guess.