One of the most exciting targets for cosmic microwave background (CMB) polarization measurements is the faint signal from the primordial gravity waves predicted by inflationary models. Currently existing experiments and those under construction would constrain or detect such a signal at around r = 0.01, where r is the tensor to scalar ratio. In order to further improve the measurement, experiments for the next generation have to combine the following three: 1) excellent sensitivity, 2) multi-frequency measurement for the removal of galactic foregrounds, and 3) well-controlled systematics. We propose the Multimoded Survey Experiment (MuSE), which uses highly multimoded polarization-sensitive bolometers developed at NASA Goddard Space Flight Center (GSFC). MuSE, consisting of 69 pixels, will achieve a sensitivity equivalent to several thousand single-moded bolometers. Each pixel can be configured to be sensitive to a different frequency band, allowing very wide frequency coverage by a single focal plane. This enables us to clean galactic synchrotron and dust components with our data alone. MuSE achieves an effective array sensitivity to the CMB of 8 μK√s even after accounting for the sensitivity degradation from foreground removal and reaches a 2-σ error on r of 0.009 with two years of operation.