The evolutionary history of human spindle genes includes back-and-forth gene flow with Neandertals:

Proteins associated with the spindle apparatus, a cytoskeletal structure that ensures the proper segregation of chromosomes during cell division, experienced an unusual number of amino acid substitutions in modern humans after the split from the ancestors of Neandertals and Denisovans. Here, we analyze the history of these substitutions and show that some of the genes in which they occur may have been targets of positive selection. We also find that the two changes in the kinetochore scaffold 1 (KNL1) protein, previously believed to be specific to modern humans, were present in some Neandertals. We show that the KNL1 gene of these Neandertals shared a common ancestor with present-day Africans about 200,000 years ago due to gene flow from the ancestors (or relatives) of modern humans into Neandertals. Subsequently, some non-Africans inherited this modern human-like gene variant from Neandertals, but none inherited the ancestral gene variants. These results add to the growing evidence of early contacts between modern humans and archaic groups in Eurasia and illustrate the intricate relationships among these groups.

The standard model is that 500-750,000 years ago the ancestors of African (modern) stem humans and Neandersovans diverged, and that’s that before the recent admixture and assimilation. But it’s pretty clear there were contacts between stem lineage and Neandersovans before the recent expansion of the African lineage. Neanderthals acquired lots of neat genes from our lineage, and we probably acquired stuff from them too.

(note that I think there were old modern lineages that disappeared)