How did Romans get water to the top of a domus

It was usually carried up in large amphorae, if it were needed. Now the Romans did have pumps and syphons, but these were used in industrial enterprises, not in private homes. Although the Romans did have houses with second stories, there was really no need for water upstairs as most of those rooms were sleeping rooms or sitting rooms. The main floor was where water was needed such as in the in the kitchens, fountains, baths, latrines, and many houses had aqueduct water piped in.