The Multivariate compound heatwaves (MCHWs) present a significant risk to human health and ecological diversity, which attract widespread attention from researchers and society. The intensity and variability of summer MCHWs over Western Europe (WE) (MCHWs_WE) have substantially increased over the last two decades. The growing chance of such events is likely related to human activity-induced climate change. However, the possible contributions from multiple atmospheric boundary forcing remain unclear. This study investigates the combined effects of North Atlantic sea surface temperature (SST), Tibetan Plateau (TP) snow cover (SC), and Arctic sea ice (SIC) on the variability of extreme summer MCHWs_WE. Observational analysis shows that an intensified anticyclonic system prevailing over WE, one of the centers of an atmospheric wave train dominating the North Atlantic-Europe sector and persists from late spring to summer, is the essential system contributing to the extreme MCHWs_WE. Spring North Atlantic SST anomalies in the form of a dipole pattern persist from spring to summer and contribute to the summer extreme MCHWs_WE by exciting a downward propagating Rossby wave train pattern. Additionally, excessive late spring SC over the western TP and SIC over the Arctic, which are stimulated by the North Atlantic anomalous SST-related wave train, can intensify the MCHWs_WE-related anticyclonic system through vertical circulation and wave energy transport. The study further quantifies the relative contributions of the aforementioned factors. The findings of this study could potentially offer valuable insights for improving the prediction skill of summer extreme MCHWs_WE. Western Europe (WE) has faced more and more multivariate compound heatwaves (MCHWs) during summer in recent decades, which pose a greater human health risk than univariate heatwaves. In this study, Our study identifies MCHWs in WE as being characterized by high temperatures and humidity, mainly influenced by a strong anticyclonic high pressure system. Furthermore, the strengthening of the MCHWs_WE-related anticyclone is a consequence of the combined impacts of preceding North Atlantic sea surface temperature (SST), Tibetan Plateau (TP) snow cover (SC), and Arctic sea ice (SIC). Spring positive dipole pattern of North Atlantic SST anomalies, exhibiting persistence from spring to summer, excite downward propagating Rossby waves. There wave trains from the Atlantic to Eurasia serve as a background field that enhances the linkage between SIC, TPSC, and the MCHWs_WE-related anticyclonic system. These factors ultimately contribute to the strengthening of anticyclones over West Eurasia (WE) through vertical circulation and wave energy transport, which jointly impact MCHWs_WE. Multivariate Compound heatwaves in Western Europe (MCHWs_WE) become more frequent in recent decades, which are linked to intensified anticyclonic system The development of the anticyclone over WE is associated with the dipole pattern of North Atlantic sea surface temperature, excess Tibetan Plateau snow cover and Arctic sea ice Combined effects of multiple forcing factors can account for approximately 40% of the variability in summer MCHWs_WE
