Yes, it is possible, but I can't answer your question regarding the existing roof's capacity. Without knowing anything about the roof structure of your home, ground snow loads, etc, if you can build a structure that adds minimal loading to your existing roof, you can do as you suggest. You will be only adding dead load, that is the weight of the materials of the new portion of the roof. Snow loading would change little.

The trick is in having the new roof load that would be directly above your current roof bear as much as possible only on the new structure. This is done by constructing the new roof in a cantilevered manner. (A cantilever is a beam or stucture that is supported at one end and at an intermediate point so that the projecting end is supported without a post at the opposite end.) Run your ridge beam in such a way that a post that bears on the new structure's wall adjacent to the existing exterior wall will provide the intermediate posting the cantilevered ridge requires.

A good rule of thumb (if such a thing exists) is to have one third or less of the cantilevered beam unsupported. That is have at least two thirds over the new addition and no more than one third over the existing roof. The depth of the beam will depend, of course, on the span and the snow load conditions. A cantilevered ridge beam will pick up approx. one half the additional roof load that would otherwise bear on your existing roof.

If you can run additional beams to cantilever over the existing roof closer to the heel of the valley rafters, you might eliminate most of the additional dead load of the the roof.

If this isn't clear, you might talk to a good framer or architect. Or you can email me and I'll try to respond as soon as possible.

Wayne