Both are grammatically correct. However, take more rest is not used commonly by native speakers. Preferable use of words is, "get some rest."

Hi Sarah, Some words naturally collocate in English. We "take a break", "give (someone) a break", "have some rest", "take a nap" and "take a vacation". Hence, I'll use ".....have more rest." I'm not saying other combinations are wrong; they just sound less natural. Cheers, Lance

Thank you dear Bex:)

I would say "get more rest". But "take a rest" when it's singular. I hope this helps! ☺️