In multimode transceivers, a local transmitter may induce a strong interference in a local receiver, often several orders of magnitude stronger than the desired received signal. To suppress this interference linearly, the receiver would need a very large dynamic range, resulting in excessive power consumption. A potentially much more power-efficient approach involves a memoryless nonlinearity that can strongly suppress the interference when accurately adapted to the envelope of the interference. This approach has so far been limited to constant-envelope interferers owing to the difficulty of extracting accurate interference envelope information from the compound received signal. In this paper, we observe that in multimode transceivers the locally available baseband interference enables accurate adaptation for varying-envelope interferences. The paper performs a system study to explore the resulting performance. Specifically, we show that for varying-envelope interferences, nonlinear distortion products emerge that are negligible for constant-envelope interferences. We analyze these products, identify the conditions for which adequate interference suppression is combined with negligible distortion, and show that these conditions are met in most cases of practical interest. Simulations for a broad set of modulation schemes corroborate this analysis.