I feel sure this has been covered here but my searching has been mostly in vain.
For the first time ever, I have a BE ticket. It was purchased by a client on my behalf (so don't blame me unless I keep working with this client

). Am I correct that there is no way to "buy up" to a regular ticket post-purchase? It's a 3.5 hour flight each way so I would pay the fare difference ($60) just for the right to select seats if I could, but I think that not being able to do so is part of the BE bargain.
Am I correct in my understanding?