句子没有问题。with me是介词短语作状语，that从句作宾语。估计你是将agree with作为一个整体接宾语me，所以that从句的成分无法划分。其实，agree常可与about, among, on, to, with等介词搭配，当agree接that引导的宾语从句时，可根据需要在agree和从句之间加适当的介词短语作状语。又如：
Without trying to decide what Hume and Locke wanted, I expect we can agree among ourselves that the most the empiricist can reasonably demand is definition of words in context, sentence by sentence.我们先不管休谟和洛克是怎么想的，但我希望在我们之间能达成共识：经验主义者能够合理要求的，最多不过是对词的逐句逐句的语境定义。