We absolutely can do so if Neal is part of the trade.
The current evolution of this thread led to:
1st 2019, 1st 2020, James Neal and Mike Smith for Schenn, Schmaltz (or perhaps Edmundson), and Jake Allen.
Blues take on Neal's contract and hope he can turn it around, while riding out smith for the remainder of the year. They get 2 1sts for value on Schenn+ the depth d included. The flames take on Allen's contract and hope he can return to better numbers as a backup to Rittich. They get out of Neal's contract while adding Schenn to really bolster their top 6 (schenn is signed for another year too, about the same salary as James Neal).
It's a steep price for the flames, but if you believe as I do that the picks will be in the 25 range it's really not that bad.