Hydrodynamic studies of stellar-mass compact objects (COs) in a common envelope (CE)have shown that the accretion rate onto the CO is a few orders of magnitude below the Bondi-Hoyle-Lyttleton (BHL) estimate. This is several orders of magnitude above the Eddington limit and above the limit for neutrino-cooled accretion (i.e., hypercritical accretion, or HCA). Considering that a binary system inside the CE of a third star accretes material at nearly the same rate as a single object of the same total mass, we propose stellar-evolution channels which form binary black hole (BBH) systems with its component masses within the pair-instability supernova (PISN) mass gap. Our model is based on HCA onto the BBH system engulfed into the CE of a massive tertiary star. Furthermore, we propose a mass transfer mode which allows to store mass lost by the binary onto a third star. Through the use of population synthesis simulations for the evolution of BBHs and standard binary-evolution principles for the interaction with a tertiary star, we are able to produce BBHs masses consistent with those estimated for GW190521. We also discuss the massive binary system Mk34 as a possible progenitor of BBHs in the PISN gap, as well as the spin distribution of the observed mergers in the gravitational-wave catalog.