The RTX 4070 can run some games at over 240 fps at lower resolutions and settings, but not all games will reach that level of performance. For example, according to some benchmarks, the RTX 4070 can run CS:GO at 1080p low settings at over 400 fps, but it can only run Cyberpunk 2077 at 1080p ultra settings with ray tracing and DLSS at around 70 fps. Therefore, if you want to use a 240Hz monitor with the RTX 4070, you may need to adjust your resolution and settings accordingly to achieve the desired frame rate.