Grafting is a valuable tool for managing problems of tomato soil-borne pathogens and pests, but often generates unpredictable effects on crop yield and product quality. To observe these rootstocks-induced changes, experimental designs including many rootstock-scion combinations are required. To this end, a greenhouse experiment was conducted on 63 graft combinations, involving seven cherry tomato scions grouped in large, medium and small-fruited, and eight rootstocks with different genetic backgrounds (crosses between Solanum lycopersicum and S. habrochaites or S. peruvianum or S. pimpinellifolium, plus an intraspecific hybrid), using ungrafted controls. The response of the graft partners was firstly analyzed individually using the environmental variance (σ2E), then by grouping them by classes. When analyzed individually, the scion genotype influenced fruit L*, b*, shape index, total soluble solids (TSS) and its ratio with tritatable acidity (TSS/TA), whereas plant growth and yield were unpredictable. After clustering the graft partners, some of these responses were attributable to the imposed classes. The S. habrochaites-derived hybrids maximized plant biomass, unlike the S. pimpinellifolium ones. Both classes reduced fruit biomass in small- and medium-fruited scions (by 11 and 14%, respectively). The S. habrochaites and S. peruvianum hybrids reduced a* and TSS, whereas promoted TA. L-ascorbic acid was reduced by grafting (from −23 to −45%), in the S. pimpinellifolium group too, indicating, even in low vigor rootstocks, a dilution effect worsening this nutraceutical trait of tomatoes.