Four museums and a contemporary art gallery are among the 16 organisations invited to apply for the second stage of the Arts Council England large capital grants programme.

The Story Museum in Oxford, Tunbridge Wells Museum and Art Gallery, Derby Museums, and Plymouth City Museum and Art Gallery are among those in line for a total of £57m.

The Institute of Contemporary Arts has applied for £1.2m to redevelop its building in central London, including improved disabled access.

The applications will be assessed for the long-term sustainability and resilience of the proposed projects, the potential for partnership funding, and whether the organisation is able to manage and deliver the work proposed.

The Story Museum is applying for £2m to help redevelop its building. Tish Francis, the museum's joint director, said: “Using our rough spaces over the past four years has taught us a lot about how best to develop the museum and this news provides real impetus to our fundraising efforts to secure the remaining match funding and bring our whole building into use by 2019.”

Tunbridge Wells Museum has applied for nearly £1m to develop a cultural and learning hub. Jo Wiltcher, the shared museums manager for Maidstone Borough Council and Tunbridge Wells Borough Council, said: “If successful at Stage 2, this funding will ensure that our current practice of working with artists, makers and creative professionals is embedded into the redevelopment of the museum and art gallery, making the hub a truly cultural venue for our visit.”

The 16 organisations will complete a stage two application over the next 18 months, which will include more detailed design plans.