You may want to use the number/letter system that is consistent with the original plant and use postscripted values for intermediate grids. Alternatively, you can start a fresh system. If the facility has a 'plant engineer' on staff that looks after day to day things, you may want to discuss this with him. When using existing grids for additions, I usually denote them differently on plan as well as the 'bubbles'; I usually use the equivalent of a hidden line or something.
Also, it is very handy to prepare a good key plan, showing all the grids for the facility. This can even be a separate sheet and may only contain grids, exterior walls, bearing walls, etc.
Also, horizontal and vertical control tied into the existing building is important (This is a real headache with some hospitals).