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Genome wide association studies of schizophrenia reveal a complex polygenic risk architecture comprised of hundreds of risk variants; most are common in the population, non-coding, and act by genetically regulating the expression of one or more gene targets ("eGenes"). It remains unclear how the myriad genetic variants that are predicted to confer individually small effects combine to yield substantial clinical impacts in aggregate. Here, we demonstrate that convergence (i.e., the shared downstream transcriptomic changes with a common direction of effect), resulting from one-at-a-time perturbation of schizophrenia eGenes, influences the outcome when eGenes are manipulated in combination. In total, we apply pooled and arrayed CRISPR approaches to target 21 schizophrenia eGenes in human induced pluripotent stem cell-derived glutamatergic neurons, finding that functionally similar eGenes yield stronger and more specific convergent effects. Points of convergence constrain additive relationships between polygenic risk loci: consistent with a liability threshold model, combinatorial perturbations of these same schizophrenia eGenes reveal that pathway-level convergence predicts when observed effects will fail to sum to levels predicted by an additive model. Targeting points of convergence as novel therapeutic targets may prove more efficacious than individually reversing the effects of multiple risk loci.