[firedrake] Solve multiple variational problems at once

Dear all, How would I solve multiple nonlinear variational problems simultaneously? For example, say that I have three residuals F(u1,u2,u3;v) = 0 G(u1,u2,u3;v) = 0 H(u1,u2,u3;v) = 0, where v is the test function. I need to solve all three of them together. Any suggestions? Thank you. Best, Anna.