How long after another beard transplant?

As you rightfully state: "it does depend on seeing your doctor since everyone is different".  In general you need to wait to see the transplanted hair grow out.  This takes 6 to 12 months.

Is a good rule to wait before having a second procedure in the same region.Perhaps even longer.  However, every doctor may have their own protocol.

You generally should wait at least 8 months to give the first transplant the opportunity to fully grow out. Then, if it is not thick enough, you can do another transplant