DfT has mandated the ITSO standard for all TOC smartcard systems so
compatibility should be ensured. However, note that the primary
intention of ITSO is that you buy a ticket and load it onto your
smartcard before travelling (although the loading could, conceivably,
be done via the gateline card reader).

ITSO is not really intended for stored value from which the cost of
your journey is deducted, although it may appear for limited,
localised applications. First of all, it would require a third party
bank to administer any scheme (despite what non-lawyer above said - if
he's got a way round the legal situation he could make himself a
fortune), and each TOC would need to agree to accept that bank's
stored value. Secondly, trying to work out the correct fare for your
PAYG journey is difficult enough on London Underground, with a fairly
simple route and fares structure, never mind on National Rail with its
mass of different routes and fares. (If you want to know what I mean,
take a journey from Gunnersbury to Hanger Lane via Turnham Green,
Ealing Broadway, and North Acton. You won't have stepped outside zone
3 but just see what fare you get charged.)