This paper develops a comprehensive asymptotic theory for implied volatility in multifactor rough volatility models, with applications to SPX and VIX options. The authors extend previous single-factor results to a general multifactor setting using Malliavin calculus, deriving explicit small-time limits for the ATM implied volatility level, skew, and curvature. The key technical innovation is the use of the Clark-Ocone formula to represent the underlying asset as an exponential martingale, enabling the application of asymptotic expansions even in non-Markovian rough volatility models. The results are applied to the two-factor rough Bergomi model, yielding closed-form expressions that reveal how parameters control the skew and curvature of both SPX and VIX smiles. This provides a theoretical foundation for joint calibration, showing that multifactor models can capture the different short-time behaviors of SPX and VIX implied volatilities, which single-factor models fail to do. The paper also includes detailed proofs and numerical examples demonstrating the effectiveness of the approach.