  In this Letter we show that multiband observations of stellar-mass binary
black holes by the next generation of ground-based observatories (3G) and the
space-based Laser Interferometer Space Antenna (LISA) would facilitate a
comprehensive test of general relativity by simultaneously measuring all the
post-Newtonian (PN) coefficients. Multiband observations would measure most of
the known PN phasing coefficients to an accuracy below a few percent---two
orders-of-magnitude better than the best bounds achievable from even `golden'
binaries in the 3G or LISA bands. Such multiparameter bounds would play a
pivotal role in constraining the parameter space of modified theories of
gravity beyond general relativity.
