Compact, broadband, and high-resolution spectrometers are appealing for sensing applications, but difficult to fabricate. Here we show using calibration data a spectrometer based on a multimode waveguide with 2 GHz resolution, 250 GHz bandwidth, and a 1.6 mm × 2.1 mm footprint. Typically, such spectrometers have a bandwidth limited by the number of modes supported by the waveguide. In this case, an on-chip mode-exciting element is used to repeatably excite distinct collections of waveguide modes. This increases the number of independent spectral channels from the number of modes to this number squared, resulting in an extension of the usable range.