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Yes, you can increase the HP a little (1 to 2 hp) by increasing the RPM, but then you run the risk of it coming from together. You can also get 5 to 15 hp gain by adding a ($$$) turbocharger but you will lose longevity. But by far the best way to increase hp is to buy a bigger tractor.
What makes you think you need a "tune-up"? Does the engine run at operating temp (≈180°F ≈82°C)? Is the radiator clean? Is the fuel clean and dry? Coolant pump belt tight? Fuel filters changed when? Oil & filter changed when? These things will all make a difference on how the engine performs.