You can absolutely tint the oil finish.
https://www.rockler.com/mixol-universal-tint-kit-colors-1-12?country=US&sid=V91117&promo=shopping&utm_source=google&utm_medium=cpc&utm_term=&utm_content=pla&utm_campaign=PL&gad_source=1&gclid=Cj0KCQjwwYSwBhDcARIsAOyL0fhvzyuqSXYKR7dz3k9BVFysImMPrvLi49h2ttN7xCJdcfYUNxeiaM0aAnSHEALw_wcB