There is a very direct translation.
If "more than" means higher degree/level of the [verb], then
I [verb] [x] more than [y] can be translated to
我 [verb] [x] 甚于 [verb] [y].
I [verb] [x] more than [y]. 我 [verb] [x] 甚于 [verb] [y].
I love you more than my phone. 我 爱 你 甚于 爱 我的手机.
甚于 means "surpass, exceed", indicating the degree/level of the [verb].
If "more than" means a larger number/amount, then 甚于 should be replaced with 多于.
I play basketball more than football. 我 玩(打) 篮球 多于 玩(踢) 足球.
You may notice that the verb appeared twice in the Chinese translation. The second verb is there to avoid ambiguity. There is no case(grammar) in Chinese. A pronoun is always in the same form whether it's accusative case or nominative case. If you say
then I don't know whether you mean
I love you more than he does. 我比他更爱你
I love you more than him. 我爱你甚于爱他.
If you are sure no ambiguity will be introduced, then you can leave out the second verb. As in
There is only one reasonable interpretation, that is
I love you more than my phone.
No one will interpret it as
I love you more than my phone does. 我比我的手机更爱你.
In this case, the second verb can, but doesn't have to, be left out. It's always OK to specify the second verb.