Thank You all for your feedbacks.
I second the idea of following the Engine Out Procedure although I was thinking that if the vibrations occur after the diversion point between the SID and the EOProc. (ie. the last common point between both) then we would need to evaluate whether to remain on the SID or rejoin the EOProc. and due consideration should be given to obstacles, MSA and SID gradients to assess the safest course of actions. Do You train this type of scenario in your operations?