It should be possible to check a bag in to pretty much anywhere that is served by commercial airlines. Getting boarding cards for the last leg from the initial airline may not be possible though, so visiting the airlines desk in DUB may be required, where you may need to hand them over a copy of the bag tags so they can add them in to their system.
For example on the DCS I currently use it's simple to add in an onward flight and print a bag tag for pretty much any airline a passenger may be travelling onwards with weather or not it's our one, a partner, a codeshare or even one which has nothing to do with us. The boarding cards will usually only come out if it's an airline in the same alliance as us or one with which we codeshare or interline with.
You should have no problem checking the bag in all the way, 2 tags will probably be printed off to enable all those airport codes in one journey, but that's fairly standard. Have all your flight numbers and bookings ready so that the agent can add them in to their system. They may also need to add eticket numbers, so have them on hand too.