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Observation of gravitational waves (GWs) in two different frequency bands is referred to as multiband GW astronomy. With the planned Laser Interferometric Space Antenna (LISA) operating in the $10^{-4}-0.1$ Hz range, and third generation (3G) ground-based detectors such as the Cosmic Explorer (CE) and Einstein Telescope (ET), operating in the $1$-$10^4$ Hz range, multiband GW astronomy could be a reality in about a decade. In this paper we present the potential of multiband observations of intermediate mass binary black holes (IMBBHs) of component masses ${\sim}10^2$-$10^3\,M_{\odot}$ to test general relativity (GR). We show that mutiband observations of IMBBHs would permit multiparameter tests of GR-tests where more than one post-Newtonian (PN) coefficient is simultaneously measured yielding more rigorous constraints on possible modifications to GR. We also find that the improvement due to multibanding can often be much larger than the best of the bounds from either of the two observatories. The origin of this result, as we shall demonstrate, can be traced to the lifting of degeneracies among the various parameters when the information from LISA and 3G are taken together. We obtain the best multiband 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 would allow 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).