From "Anna (Go To Him)":
"You say he loves you more than me, so I will set you free; go with him."
and from "If I Fell":
"If I give my heart to you, I must be sure, from the very start, that you will love me more than her."
Colloquial grammar is ok as long as it's unambiguous, and I have nothing against bisexuality, but the grammatical interpretation here just isn't Beatles!
Remember, when in doubt over a comparative sentence, write it out fully and then chop off the unnecessary bits:
"You say he loves you more than I
"You say he loves you more than