Agile Teams with continuous changing team members of operations

I want to transform the current ITIL based team structure (with Plan, Build and Run focus) to an agile team organization. One key challenge is to make continuous shifts between Operation team and different build teams possible. 

Is such an organization possible at all? What could such an organization look like and how can such a change be organized? 

in facts: 50 employees
OP team has 25 employees. All other should be in 4 agile teams

thx

Patrick