ALMA 870 μm continuum imaging has uncovered a population of blends of multiple dusty star-forming galaxies (DSFGs) in sources originally detected with the Herschel Space Observatory. However, their pairwise separations are much smaller than what is found by ALMA follow-up of other single-dish surveys or expected from theoretical simulations. Using ALMA and the Very Large Array, we have targeted three of these systems to confirm whether the multiple 870 μm continuum sources lie at the same redshift, successfully detecting 12CO (J = 3–2) and 12CO (J = 1–0) lines and being able to confirm that in the three cases all the multiple DSFGs are likely physically associated within the same structure. Therefore, we report the discovery of two new gas-rich dusty protocluster cores (HELAISS02, z = 2.171 ± 0.004; HXMM20, z = 2.602 ± 0.002). The third target is located in the well-known COSMOS overdensity at z = 2.51 (named CL J1001+0220 in the literature), for which we do not find any new secure CO (1–0) detection, although some of its members show only tentative detections and require further confirmation. From the gas, dust, and stellar properties of the two new protocluster cores, we find very large molecular gas fractions yet low stellar masses, pushing the sources above the main sequence (MS), while not enhancing their star formation efficiency. We suggest that the sources might be newly formed galaxies migrating to the MS. The properties of the three systems compared to each other and to field galaxies may suggest a different evolutionary stage between systems.