The only difference over a pure domestic itinerary at the first stage is that there will be a bit of extra time at the check in desk if (a) you have some weird through-check-in problem with a partner airline down route that day and (b) visa/passport checks.
The other thing is that the "three hours required" thing is a bit of a myth.
In some airports, particularly where there are lengthy, bureaucratic and chaotic exit controls (India, parts of South America) then you really will need that much time at the international exit point. But you certainly wouldn't at the domestic part of the journey.
In my personal experience; in Europe or the US, where taking an international plane is not much different to taking a city bus, it is rare for me to be at the airport more than sixty minutes before departure. Life is too short to spend it at the airport.
If you are checking a bag many airports will not accept economy passenger baggage more than three hours ahead anyway.
The main reasons, I think, for the "three hour recommendation" is (a) so you cannot blame the airline's guidance if you arrive at the airport slightly too late and (b) to give you more time to do shopping in the airport. On those two points you probably will be "recommended" to appear as early as possible.