I'd like to meet as many of his requests as I can.
I'll try my best to meet his demands.
この場合、次のような言い方ができますよ。
ーI'd like to meet as many of his requests as I can.
「出来るだけ彼の要望に応えたい」
to meet one's requests で「人の要望に応える」と言えます。
ーI'll try my best to meet his demands.
「彼の要望に応えれるようにする」
to meet one's demands でも「人の要望・要求に応える」と言えます。
ご参考まで!