The aim of this study is to examine the daily return spillover among 18 cryptocurrencies under low and high volatility regimes, while considering three pricing factors and the effect of the COVID-19 outbreak. To do so, we apply a Markov regime-switching (MS) vector autoregressive with exogenous variables (VARX) model to a daily dataset from 25-July-2016 to 1-April-2020. The results indicate various patterns of spillover in high and low volatility regimes, especially during the COVID-19 outbreak. The total spillover index varies with time and abruptly intensifies following the outbreak of COVID-19, especially in the high volatility regime. Notably, the network analysis reveals further evidence of much higher spillovers in the high volatility regime during the COVID-19 outbreak, which is consistent with the notion of contagion during stress periods. © 2021, The Author(s).