Although some will do it, recommendations with too little information usually doesn't solve the problem. I recommend you try various things to gain e xperience with what difference they make. While you shop for more equipment, sharpen the blades. If you aren't certain how blades should be sharpened, remove and take them to a professional. Before removing blades, look close to see if they turn cw or ccw. DON"T EVEN THINK about looking under deck while tractor id running. It's easy to tell which way blade has been turning by shiny edge. You might find the problem to be blades installed up-side-down following last time they were sharpened. Take notice of angle which pro ground blade so you know how much angle to use when you grind them next time. Park on level surface,set mower to preferred height then using ruler,tape or blocks of wood, adj so that right and left are same (level). Set front of deck 1-2" lower than rear, that's right, all rotary mowers are supposed to be lower in front (1/4-1/2" on push mower) ( 1/2-3/4" on lawn tractor). Sharp blades make a world of difference.
Here's some of those trial and errors for gaining knowledge. Use same throttle setting but next lower gear to reduce ground speed. On outer perimeter farthest from home, lift deck so it leaves grass longer on 4 or 5 passes. Notice whether grass clumps less. After deck has been dropped to customary height AND ground speed is reduced, take note of whether there's less grass clumping.
After 3-5 days you may very well find grass mowed higher looks as good and possibly better than that cut lower.