As Capt Claret said,
You need more blades to "absorb" the extra power being provided. The curved tips reduce transonic effects, which reduce efficiency and increase noise.
When the engine is more powerful, you need more "solidity" to the prop disc: either increasing blade area, number of blades or prop speed. Increasing prop speed creates problems with the tip speed and efficiency, and wider blades are heavier and less efficient as well (think aspect ratio of the blade).
If you can, have a look at the different props used on the spitfire from the prototype (~1000hp, two bladed prop) to the latter development trials (~2200hp). I don't think they got past six blades because the hub becomes an engineering/maintenance nightmare. Those were all straight metal props, but now composite materials allow more efficient curved designs.