Is it possible at all to do a cash upgrade on an Avios award ticket booked through BA
 

Booked two EL award tickets end of June 2019 for economy, JFK-SNN. Is it possible to offer cash to upgrade? I don't think they'll open more business availability for awards which I know I could upgrade using more Avios but I'm not sure.

I booked by transferring MR to BA and then booking over the phone to get cheaper taxes/fees.

if you mean bid for upgrade through the EI (aer lingus) site, the answer is no. Reward tickets are excluded from bid for upgrade. EI dont tend to offer cash upgrades at the airport (years ago they used to offer upgrades ex-USA to DUB on some flights if there were seats available, not never ex-DUB or SNN)

Only revenue tickets can be upgraded and typically they will have to be sold by EI themselves

It is unlikely EI will make further reward seats available