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We prove the existence of piecewise smooth MHD equilibria inthree-dimensional toroidal domains of $\mathbf{R}^3$ where the pressure isconstant on the boundary but not in the interior. The pressure is piecewiseconstant and the plasma current exhibits an arbitrary number of current sheets.We also establish the existence of free boundary steady states surrounded byvacuum with an external surface current. The toroidal domains where theseequilibria are shown to exist do not need to be small perturbations of anaxisymmetric domain, and in fact they can have any knotted topology. Thebuilding blocks we use in our construction are analytic toroidal domainssatisfying a certain nondegeneracy condition, which roughly states that thereexists a force-free field that is ergodic on the surface of the domain. Theproof involves three main ingredients: a gluing construction of piecewisesmooth MHD equilibria, a Hamilton-Jacobi equation on the two-dimensional torusthat can be understood as a nonlinear deformation of the cohomological equation(so the nondegeneracy assumption plays a major role in the correspondinganalysis), and a new KAM theorem tailored for the study of divergence-freefields in three dimensions whose Poincar\'e map cannot be computed explicitly.

MHD equilibria with nonconstant pressure in nondegenerate toroidal domains