In my experience, it is not possible to implement a personalized solver in COMSOL. However, as a work-around, the matrix and the vector could be extracted via MATLAB Livelink. Although it is not a great option, this would at least allow you to design your own solver in MATLAB.
I agree with Ritukesh Bharali here. The only way known to me would as well be to use the Livelink to Matlab. However, the question about the numerical stability remains open and I am not sure that it is worth the effort, but this is my personal opinion.