1.该问句变成陈述句是：you are/I am going to do what with that vase.
2.do with短语的完整写法是：do sth with sth.
所以,what是do的宾语,并非that vase的宾语补足语.
3.该短语do sth with sth比较特别,第二个sth指的是具体的事物,而第一个sth一般是something/nothing/nothing/more/little/a little/a lot这样的不定代词,对上述代词提问时,也还是用what提问.
4.如：
1）I can do nothing with this problem.
2) I want to do something with the case.
5.类似的短语还有know/learn sth with sth.
如：I'd like to know more about your school.