You can extend a masonry chimney as long as you follow the codes. The base must be capable of supporting the total weight. The connection to the house proper must still maintain a 1 inch clearance to combustibles. The flue tiles must be properly sized, installed, with the proper mortar and carried up ahead of the brick. Due to the circumstances, I think a Level II is certainly in order here. For one, it looks a little short.

If you are going to do this one, you'll need to do the heater flue at the other end of the house. That had to be extended, too didn't it?
Bob

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