Let \Gamma be a definable class of forcing posets and \kappa be a cardinal. We define MP(\kappa,\Gamma) to be the statement:

"For any A\subseteq \kappa, any formula \phi(v), for any P \in \Gamma, if there is a name \dot{Q} such that V^P models "\dot{Q}\in \Gamma + dot{Q} forces that \phi[A] is necessary" then V models \phi[A],"

where a poset Q \in \Gamma forces a statement \phi(x) to be necessary if for any \dot{R} such that V^Q \vDash \dot{R} \in \Gamma, then V^{Q\star \dot{R}} models \phi(x). When \Gamma is the class of proper forcings (or semi-proper forcings, or stationary set preserving forcings), we show that MP(\omega_1,\Gamma) is consistent relative to large cardinals. We also discuss the consistency strength of these principles as well as their relationship with forcing axioms. These are variants of maximality principles defined by Hamkins. This is joint work with Daisuke Ikegami.