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You do realize that there's >100 years of research on this topic about human cognitive abilities/intelligence? Reading this literature requires some understanding of statistics, but you would do well to read Stuart Ritchie's, Deary's or Haier's recent book length summaries of the area. Arthur Jensen's book is the best, but it's not an easy read.

Multiple selection is discussed in the animal breeding literature. See e.g. this review.

Samorè, A. B., & Fontanesi, L. (2016). Genomic selection in pigs: state of the art and perspectives. Italian Journal of Animal Science, 15(2), 211–232. doi.org/10.1080/1828051X.2016.1172034

Sometimes the traits selected for are negatively genetically correlated. This slows down the process, but does not make it impossible unless the genetic correlation is -1.00. For humans, most of the traits we want seem to be positively related, with a few exceptions. Sometimes bipolar and IQ have positive relationships, which may be undesirable. Bipolar is associated with creativity however, so perhaps it's not entirely bad. A larger problem is the negative genetic correlation between fertility and IQ. There's also myopia and IQ.