应该没有什么区别,但用for 比较多:
Did you come to Paris for the purpose of seeing your family, or for business purposes?
你到巴黎来是为了和家人团聚呢,还是为了办公事?
He came here for the purpose of borrowing money from you. 他特地来这里是向你借钱。
I came with the express purpose of seeing you. 我特地来看你。
They came here with the purpose of making trouble. 他们到这儿来就是为了找麻烦的。
查了一下《牛津英语搭配词典》
这两种搭配是写在一起的,所以没区别
for/with purpose of
为了/有...的目的
例句: The school was founded with/for the express purpose of teaching deaf children to speak.
学校创建时就有明确的目的,即教耳聋的孩子学会说话。