It would be slightly better to use "further" here:

"A further concession on our part is unfortunately not possible."

Any further...?

Ich denke nicht, dass 'ein' hier '1' bedeutet. Ich würde es allgemeiner halten.

heißt es dann so:
Any further concessions on our part are unfortunately not possible?

"Unfortunately we are unable to make any further concession."

-- makes it a little bit less particular.

"concession" is countable, in the way that "Entgegenkommen" isn't. You can't really get round that problem by using the plural. Unless plural concessions are in fact involved. Context.