As the others have said, this is not possible from what I have seen as well...
May I ask why you need to migrate the data to a new suite?
If you want all the existing data, why are you creating a new suite?
If you are re-making your site, or migrating to a new code platform for your website, you can continue to use the existing suite (sending equivalent data from the new site into the existing dimensions, and letting other no longer relevant dimensions gracefully fade out of existence)
If you are splitting you site into two, i.e. creating a new domain for a branch, you probably don't want the full data carried over to the new offshoot anyway... and while this will make before/after trending more difficult, the new site can start with a clean slate... If you do need to compare before/after, you can use Report Builder to pull segmented data from the old suite (for site X) and the new Site X data, and use Excel to merge the data into a single table that shows before and after, then you can graph all the data to see the trending.