Which you use depends on the context. A conversation might go like this: "I would like some more juice." (Someone gives you some juice and you drink it all and come back with an empty cup and say, "I would like even more juice.") In other words, you've already asked for more and now you want more again, or "even more." Another typical conversation might be if you said that Susie looks like her mother. Then someone else said, "But have you seen Susie's older sister Becky? She looks even more like her mother." In other words, you are comparing two things that both share a certain quality but one has "even more" of this quality.