Driver with Panther here... ina straight truck with a tag axle. First to answer your question of will 3 axles increase your profits, simply put-yes.
Dave is correct though, if you're the type to refuse alot or a little...yes your profits will suffer. Refuse as few loads as possible, thats the key. The old saying is: you gotta take the garbage to get the good stuff.
What I would suggest is getting a truck (or in a truck) that has a "liftable" tag axle. I have to put my tag down on anything over 8,000 lbs., and I've found myself hauling a fair amount of loads in the past in the 9,000 to 11,000+ lbs. range. The tag axle will make you money. When I get "heavy loads" offered to me, that's generally the range it seems. In Expediting, a vast amount of your loads in a straight truck are less than 3,000 to 5,000 lbs.
Why a liftable tag axle? well, how often do you want to buy 4 new tires? Why pay for tread wear when technically you don't really need to? Pay for the tread wear when you get the loads that require you to use that axle. Those tags scrub sideways on turns and you'd be lucky to get 25K miles out of them if you kept them down all the time. Plus, they won't help you if you're in snow or muddy conditions, actually they will impede you. I got caught in some heavy snow and had 8,500 lbs. in the box (to cross scale legally loaded over 8,000 lbs. I have to have my tags down), well I got into a parking lot that had some big puddles with ice and snow in them. I started to get stuck in one large deep puddle-I reached down and hit the knob to pull up my tags...rocked the truck some and pulled right out. I might have had to call a tow truck if my tags were not liftable. By pulling up the tags in that scenario I was able to give the drives more traction (by putting more weight on them) and therefore able to save myself from a tow truck bill of probably $200 plus. So, do my tags make me profitable-yes.
Another scenario: if you're in a 2 axle truck with a max of 10K lbs payload capacity and I'm parked right next to you...you get a load offer for a load of 10,500 lbs., you gotta turn it down 'cause it's too heavy. I just made money by simply pushing a knob in on my dash. I love it, I really do. Most of the time I keep it up though-but it's sure nice to have.