Context. Over the past 15 years, studies of quasars in the far-infrared (FIR) have reported host luminosities ranging from 1012 to 1014 L⊙. These luminosities, often derived from Herschel/SPIRE photometry, suggest star formation rates (SFRs) of up to several thousand M⊙ yr‑1, positioning them among the most luminous starburst galaxies in the Universe. However, owing to the limited spatial resolution of SPIRE, there is considerable uncertainty regarding whether the FIR emission originates from the quasar itself, nearby sources at the same redshift, or unrelated sources within the SPIRE beam. To resolve this uncertainty, high-resolution observations at wavelengths close to the SPIRE coverage are required to pinpoint the true source of the FIR emission. Aims. The aim of the present work is to unambiguously identify the submillimetre (submm) counterparts of a statistical sample of FIR bright SDSS quasars and estimate the real multiplicity rates among these systems. We study the evolution of the incidence of multiplicities with redshift, FIR properties, and 'balnicity'. Based on these multiplicities, we assess the importance of mergers as triggers for concomitant accretion onto supermassive black holes (SMBHs) and extreme star formation. Methods. We conducted ALMA Band 7 continuum observations of 152 SDSS FIR bright quasars in Stripe 82, covering redshifts between 1 and 4, with a spatial resolution of 0.8″. We identified all sources detected in the Band 7 maps at or above 5σ and performed forced photometry on the phase centre for the few quasars that were not detected otherwise. Additionally, we examined the coarse Band 7 spectra for any serendipitous detections of CO and other transitions. Results. We find that in approximately 60% of all cases, the submm emission originates from a single counterpart within the SPIRE beam, centred on the optical coordinates of the quasar. The rate of multiplicity increases with redshift, rising by a factor of ∼2.5 between redshifts 1 and 2.5. The incidence of multiplicities is consistent among broad absorption line (BAL) quasars and non-BAL quasars. The multiplicities observed in a fraction of the sample indicate that, while mergers are known to enhance gas inflow efficiency, there must be viable alternatives for driving synchronous SMBH growth and intense star formation in isolated systems. Additionally, we report the serendipitous detection of two CO(6–5) and three CO(7–6) transitions in five quasars at redshifts between 1 and 1.4, out of the eight such transitions expected based on the spectral setup and the redshifts of the objects in the sample. Higher transitions, although expected in a fraction of the sample, are not detected, indicating that the quasars are not sufficiently exciting the gas in their hosts. Finally, we also detect a potential emission of H2O, HCN (10–9), or a combination of both in the spectrum of a quasar at redshift 1.67.