If I have connecting flights and want to bring more luggage than hand luggage, I check one suitcase and bring a carry-on bag.
This carry-on bag is a computer bag (no wheels) that can be attached to the long handle of the suitcase so that it is easy to transport both pieces of luggage to/from airport.
In this carry-on bag I pack all essentials + enough clothes to last me 2-3 days at my destination and then I expect my lost suitcase to show up within that time frame.