Yes you can, but it's almost never a good idea, so you have to have a really good reason to try it. Here are the problems
- As Vagish pointed out, if there is any delay on your incoming flight, you will miss your connection and the second air line will treat this as your fault. Most will charge you a change fee plus potentially any difference in ticket prices which can be substantial since you are in essence buying a new ticket on short notice. If your miss a connection on a single itinerary, the air line will re-book you free of charge, absorb any price differences in tickets and put you up in a hotel overnight, if that's necessary. In the two airline scenario you are on your own for all of these.
- When arriving you have to fully clear customs and immigration. So you need a full entry Visa (transit Visa may not be enough) and collect all your bags. The problem is that you need to go to the check in counter of the second airline, which typically is in Ireland proper and not in the transit area
- Different airlines use different terminals and sometimes even different airports (happened to me in New York once) so there can be a fair bit of extra transportation (with all your bags in tow).
- It's typically way more expensive.
So you need to have a really good reason to do this, make sure you have all the right Visa and immigration documents for BOTH the final destination and transit country and you need LOTS and LOTS of time for making the connection. 6 hours minimum, I'd say. 8 hours would be safer.