Multivariable Mendelian randomization (MVMR) is widely used to estimate the causal effects of exposures on disease outcomes. However, its applications have been largely limited to individuals of European ancestry, due to the larger sample sizes available in European genome-wide association studies (GWAS). Although methods that jointly analyze multiple ancestries have been proposed to improve power in MR analyses, most of them have focused on univariable MR, which estimates total rather than direct causal effects, making them less suitable for disentangling the independent contributions of multiple, potentially correlated exposures. Here, we introduce MRBEE-TL, a novel MVMR method that combines transfer learning with bias-corrected estimating equations to improve power in underpowered ancestries and to assess cross-ancestry heterogeneity of disease risk factors. In simulations, MRBEE-TL consistently outperformed MR methods that relied solely on ancestry-specific GWAS data, achieving superior estimation accuracy, statistical power, and Type I error control. In real data analyses, MRBEE-TL not only identified ancestry-consistent and ancestry-specific causal effects missed by conventional approaches, but also improved power in African and East Asian ancestries.