You might call it the night watch: in an attempt to make space for extra visitors to the Vermeer exhibition at the Rijksmuseum, the museum is opening until 2am on its last weekend.

The blockbuster Vermeer exhibition, which now has 27 of the Dutch artist’s 37 extant works, is releasing more than 2,600 extra tickets for its final weekend on June 2 and 3.

Visitors can apply for a computer-generated random selection process, ‘supervised by a notary’, by 5pm Dutch time on Friday 12 May via the Rijksmuseum website. The lottery process asks for a date of birth and country of origin.

The exhibition, which has garnered rave reviews in international papers, sold out within three days of opening in February. It was described by director general of the Rijksmuseum Taco Dibbits as a ‘now or never’  moment, uniting paintings from all around the world.

There were murmurs about the labelling of a disputed Vermeer painting, Girl with a Flute as ‘attributed here to Johannes Vermeer’, and some people were unhappy to learn that the Girl with a Pearl Earring was only on loan for eight weeks before returning to its home at the Mauritshuis in The Hague.

But these hiccups have not stopped visitors from all over the world crowding in to see the show, praising the museum’s slick operation and imaginative hanging of the paintings amid a domestic setting of floor-length velvet curtains. Ticket sales have already been increased once, and ‘snapped up in just a few days’, according to a press spokesman.

There were rumours that the Rijksmuseum would do all it could to increase opening hours, after it had to temporarily close its ‘friends’ scheme to new applicants when it became clear this was the only way to get a ticket. Friends are able to see the Vermeer exhibition at any time, bringing a child or even a guest if they have a partner membership.

People who win the last open lottery will be notified by email by May 16 and will have a chance to buy a maximum of two tickets for an evening start time on Friday 2 June between 21.30 and half past midnight or at the same times on Saturday 3 June.