Thank you all for your replies.

looks like I was not clear enough in my original post, so I will try to clarify.

My preferred airline does not fly to my ultimate destination, but they do fly half-way to Europe. I can book on another airline from Europe to my ultimate destination but neither airline allow me to do that in one ticket on their web site (even though both are member of Star Alliance). My question was... can I make separate reservations on my own without much of a hassle??

from the replies it seems that if I do it on my own I would have trouble with luggage or connections.... so, is my only option is dealing with a travel agent??