Yes, RepricerExpress can be setup to beat Buy Box Merchants only.
In RepricerExpress - go to the Amazon Settings screen (from Pricing Settings menu). Whether you are using Basic or Advanced pricing rules - you have Setting 2 which allows you to compete with Competitors or Buy Box options. To only compete with Buy Box merchants then ensure Setting 2 is changed to the Buy Box option.
N.B. Only the lowest buy box price per condition is currently returned by Amazon so you will compete against them. If you can't beat the lowest buy box seller - the 'Best Price' option is not possible in this scenario so you will list at min.
if you have multiple rules - you will need to update each rule if you want it applied to all rules/products.