Well, one way would be to
1) First lay the footings and colomns in the extension area
2) then knock of the wall
3) underpin or scaffold the beams/girders above the wall
4) drill into the outer face at the joints of beams, coloumns from where the extension is to be done
5) drive in new reinforcement bars onto the drilled holes and grout
6) bend them up to make a crank extension
7) do the same to the new colmns
8) put up the formwork for beams and cast them with crank reinforcement, put up the formwork for floors or roof and cast them in the same way
9) build walls, doors, panels, etc at the new open faces after extension.
PS : This is just a suggestion. It’s not tried and tested. For a cost estimate, a contractor or estimator might help.