As others have pointed out, it is possible. I just redeemed 3J and 3Y tickets last week on the same flights (7 segments) using US miles and UA miles for travel to Europe and Japan in the first half of July. However as you probably know, you do need miles in same alliance to get those tickets. Buildup your point balances and try to concentrate in a single alliance to get 4J tickets.

While searching for tickets don't forget to look in to opposing alliance hubs. For example DL tix from FRA-DTW and UA tix from IAH-AMS etc. Good luck.