If I understand what you're doing, you should be using the "Groups" function in Visio.
So, after creating your multiple processes, manually select them (CTRL-left click), and then place them all into a group by selecting: Shape --> Grouping --> Group. (Or CTRL-SHIFT-G).
As you add more and more processes, you can individually add each new process to the group you created (in the above step) by selecting the new process and the group (by selecting any one item in that group) and then selecting: Shape --> Grouping --> Add to Group.
Once your group has been created, you can move the entire group as one object rather than each individual new object (process).