So if the cell formula now is, for example, summing two other cells, like:
cell A1 contains the formula =SUM(B1:B10);
and you wish to include that sum into the new total, the cell formula of cell A1 would now be: =Sum(B1:B10)-COUNTIF(D16:D380,"H")
I hope this is what you are looking for. I have tested it and it works.