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We present spectroscopic experiments and theory of a quantum dot driven bichromatically by two strong coherent lasers. In particular, we explore the regime where the drive strengths are substantial enough to merit a general non-perturbative analysis, resulting in a rich higher-order Floquet dressed-state energy structure. We show high resolution spectroscopy measurements with a variety of laser detunings performed on a single InGaAs quantum dot, with the resulting features well explained with a time-dependent quantum master equation and Floquet analysis. Notably, driving the quantum dot resonance and one of the subsequent Mollow triplet sidepeaks, we observe the disappearance and subsequent reappearance of the central transition and transition resonant with detuned-laser at high detuned-laser pump strengths and additional higher-order effects, e.g. emission triplets at higher harmonics and signatures of higher order Floquet states. For a similar excitation condition but with an off-resonant primary laser, we observe similar spectral features but with an enhanced inherent spectral asymmetry.