Yes, but the whole principal of ITSO is that you do not need more than one ITSO card. It is possible to load on any companies product onto any ITSO card - even loading a Southern 'The Key' product onto a 'Stagecoach Smart' card.
TP
This was the intention of smartcards, however at present I understand that stagecoach smartcards are effectively 'locked' to stagecoach buses, and the key locked to go-ahead buses/trains.
If there has been movement in this area, then I'd be pleased to hear updates.
Thomas Cairns, whom I understand to be a senior manager at ITSO, blogged about this issue earlier in the year http://thomas-cairns.co.uk/2012/01/fragmentation-interoperability-ticketing/