Yes, polygenic sex determination is a thing!

The process of sexual development in animals is modulated by a variety of mechanisms. Some species respond to environmental cues, while, in others, sex determination is thought to be controlled by a single 'master regulator' gene. However, many animals respond to a combination of environmental cues (e.g., temperature) and genetic factors (e.g., sex chromosomes). Even among species in which genetic factors predominate, there is a continuum between monofactorial and polygenic systems. The perception that polygenic systems are rare may result from experiments that lack the statistical power to detect multiple loci. Intellectual biases against the existence of polygenic sex determination (PSD) may further arise from misconceptions about the regulation of developmental processes and a misreading of theoretical results on the stability of polygenic systems of sex determination.