The Ashmolean Museum in Oxford could be expanded again to create more exhibition space.
The museum, which dates back to the 17th Century, plans to expand the Egyptian and Ruskin collections into space partly occupied by the shop.
If the £5.25m plans are approved, part of the Grade I listed building will be demolished to make way for lighting, showcases and gallery redesign.
The museum was reopened by the Queen last year after a £61m refurbishment.
The new plans submitted to Oxford City Council say the existing Egyptian collection is "crammed into a series of dark, confusing galleries".
The new plans would bring natural light in and "make it easier for the visitor to directly engage with and understand the collection," said architects.
Building work could begin in 2011, a museum spokeswoman said.