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Drum-like membrane resonators are intriguing for precision sensing because their resonance frequencies can be sensitive to a variety of parameters of interest, from mass to thermal radiation. The quest for improved sensitivity faces a tradeoff in which a high amplitude of mechanical motion improves signal-to-noise, but too high of a drive (beyond the so-called critical amplitude) introduces nonlinear effects. In our work published in , we develop a straightforward method to evade this tradeoff. Using a patterned, trampoline-shaped membrane, we find that dual-mechanical-mode operation can achieve a thermally-limited frequency stability.Ìý By correcting for frequency noise arising at high amplitude, we maintain this high stability when operating beyond the linear regime, opening new opportunities for membrane frequency sensing.