Can a non-deterministic machine merge its branches?

Does an NDTM have the power to combine computational branches ie. can a result from branch A be used in the next step in the computation along branch B? Can branches use each others’ results, diagrammatically ‘merging’?

Example:

Branch i arrives at the number b after n steps, branch j arrives at the number c after 2n steps. After both have arrived at their respective values (we have waited 2n steps) I want the computer to multiply 3*5 (the results from the different branches). Can I do this?