Leaving AMA with concern for meningitis

Hi all, got report of an interesting scenario from one of our ED pharmacists today. 40 yo patient presents with some classical meningitis symptoms, neck rigidity, fever, headache. ED attending had reasonable concern for meningitis, however patient wasn't really altered and left AMA without LP. Trying to give the guy the best shot despite leaving, what antibiotics would you consider here? Linezolid + doxy? Levofloxacin? Some other combination? Nothing and hope he represents elsewhere? Thought it was an interesting scenario from an ID/pharmacokinetics standpoint

Edit: assuming he's also refusing any iv abx