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Observation of gravitational waves (GWs) in two different frequency bands isreferred to as multiband GW astronomy. With the planned Laser InterferometricSpace Antenna (LISA) operating in the $10^{-4}-0.1$ Hz range, and thirdgeneration (3G) ground-based detectors such as the Cosmic Explorer (CE) andEinstein Telescope (ET), operating in the $1$-$10^4$ Hz range, multiband GWastronomy could be a reality in about a decade. In this paper we present thepotential of multiband observations of intermediate mass binary black holes(IMBBHs) of component masses ${\sim}10^2$-$10^3\,M_{\odot}$ to test generalrelativity (GR). We show that mutiband observations of IMBBHs would permitmultiparameter tests of GR-tests where more than one post-Newtonian (PN)coefficient is simultaneously measured yielding more rigorous constraints onpossible modifications to GR. We also find that the improvement due tomultibanding can often be much larger than the best of the bounds from eitherof the two observatories. The origin of this result, as we shall demonstrate,can be traced to the lifting of degeneracies among the various parameters whenthe information from LISA and 3G are taken together. We obtain the bestmultiband bounds for an IMBBH with a total redshifted mass of $200\,M_{\odot}$and a mass ratio of 2. For single-parameter tests, this system at 1 Gpc wouldallow us to constrain the deviations on all the PN coefficients to below $10\%$and derive simultaneous bounds on the first seven PN coefficients to below$50\%$ (with low spins).

Tests of general relativity using multiband observations of intermediate mass binary black hole mergers