You know that saying "if you want to find love, stop looking for it"..well, same concept. You'll get more solo's if you stop trying for solos. Why? Because many solo's occur when a player decides to throw you the solo because they really like you or really dislike somebody else. Possible they've just been stabbed and revenge is more important then winning, could be because they're grown apathetic about the game or lost confidence in their chances and want to see the person they feel most deserving win, sometimes it's just because they just had such an enjoyable experience working with you that they decide "screw it..i don't want to join the other guy to get in your way, this was fun enough". This is really the best way.
But that's not always available of course, so it's about how you approach it. I rarely play with a solo mentality, i try to enter a game completely focussed on getting to the end for a two-way. Get an ally who fits a certain mold (not difficult to work with, not the type to push for a three-way the minute you're down to three, friendly, easy going, like-minded) and treat them good, be loyal, and win your victories triumphantly. Work towards the end in good faith while paying heavy attention to ensure your not vulnerable anywhere. Treat is as if worst case you end up with a two-way..but if it falls in your lap then of course you take it. If you're good enough that opportunity comes more often then not.