This can very easily be done. I see this happening by quaternizing the amine with Methyl Iodide, then treatment of that salt with a Palladium0 species to deallylate. Careful handling will be required to achive high yields though.
In the methylation step, you would need to make the competition favor the alkylation of the amine. This is not that hard because the rate of alkylation is:
kR3N/kROH @ pH7 = ~500-1000
This means keeping the raction neutral, and using <=1eq. MeI. Otherwise, you would need to protect the alcohol and phenol as the acetate esters (Ac2O), and then saponify afterwards (K2CO3). The removal of the acetates might not be neccisary because that compound is probably just as active.
The quaternary salt from the previous reactiong will need to be dissolved in a solvent like DMF, and deallylated with a Palladium compound like Pd(PPh3)4 or Pd2(dba)3.