We present new ALMA band-7 data for a sample of six luminous quasars at , powered by fast-growing supermassive black holes (SMBHs) with rather uniform properties: the typical accretion rates and black hole masses are and . Our sample consists of three "FIR-bright" sources, which were individually detected in previous Herschel/SPIRE observations, with star formation rates of , and three "FIR-faint" sources for which Herschel stacking analysis implies a typical SFR of ∼400 . The dusty interstellar medium in the hosts of all six quasars is clearly detected in the ALMA data and resolved on scales of ∼2 kpc, in both continuum ( ) and line emission. The continuum emission is in good agreement with the expectations from the Herschel data, confirming the intense SF activity in the quasar hosts. Importantly, we detect companion sub-millimeter galaxies (SMGs) for three sources-one FIR-bright and two FIR-faint, separated by and from the quasar hosts. The -based dynamical mass estimates for the interacting SMGs are within a factor of ∼3 of the quasar hosts' masses, while the continuum emission implies . Our ALMA data therefore clearly support the idea that major mergers are important drivers for rapid early SMBH growth. However, the fact that not all high-SFR quasar hosts are accompanied by interacting SMGs and the gas kinematics as observed by ALMA suggest that other processes may be fueling these systems. Our analysis thus demonstrates the diversity of host galaxy properties and gas accretion mechanisms associated with early and rapid SMBH growth.