They will advise the RSC on how to proceed with the £100m redevelopment of its Stratford-upon-Avon site.
The two practices will investigate whether parts of the Royal Shakespeare Theatre can be retained, including its grade II-listed main staircase.
A feasibility study by the RSC last October recommended that the theatre, which was built in 1932, should be demolished.
Edward Jones, principal of Dixon Jones, emphasised that the two firms would not be taking over from the team working on the redevelopment, which includes Dutch architect Erick van Egeraat.
Jones, whose practice has worked on high-profile schemes at the National Portrait Gallery, said: "In no way are we gazumping anyone. Our role is, I suppose, almost a second opinion."
Jones said the firms would be looking at problems identified with the theatre block, such as the auditorium and backstage facilities.
He said: "We have just started. Perhaps by keeping a bit of this and a bit of that you might have a glorious compromise."
An RSC spokesperson said the two architects were undertaking a four-month study before it lodged a planning application for the scheme. Demolition of a listed building needs special planning consent.
The spokesperson said: "We are in dialogue with English Heritage and the local planning authority as to what extent retaining some or all of the theatre is consistent with what we wanted to do with the redevelopment."
The step was backed by EH, which had criticised the demolition plans. A statement said: "We welcome the fact that the RSC has undertaken a further study of the building to investigate options.
"We do not consider that the feasibility study takes proper account of our advice and believe that the case for demolition has not yet been made."
The RSC's plans for the Stratford complex include adding 650 seats to the Other Place mini-theatre and refurbishing the Swan Theatre.