Is it possible to recover data after reformatting from NTFS to Ext4?

Unlikely. Offer to contact the companies seriously involved in the restoration data. Perhaps then, stretched...

If you reformat the partition back to NTFS and then run a sector-by-sector scanning, the data can be restored.
For example, you can help a utility eSupport Undelete Plus mode RawScan with maximum quality.
But I warn you immediately: it's pretty long. Partition on the 2TB scanned 6 hours somewhere.

If you just reformatted and haven't recorded anything — R-Studio try. I was helped in this case, but I still partitions created and changed their sizes until I calmed down and remembered the data on the screw.

Runtime GetDataBack try rescued more than once, recovered ~80% of the information after formatting and installing XP over the top. But it is as lucky.

had the same situation, only data on ext4 was a bit
restored program DMDE, it found an NTFS partition and restored the old
use not to search for files and to search for topics, everything depends on the amount of recorded information after formatting in ext4, most importantly, the layout was fast and not full

someone here wrote that you want to format back to NTFS, this is a very evil man) never record data if you want to pull old