Does the amount of solute affect rate of solvation? I know that in order to increase the rate of solvation, you need to increase how often solute and solvent particles come into contact.

You can do it by:


agitating the mixture
increasing the surface area of the solute
heating up the solvent


But my question is: Does adding more solute (like adding more salt to water) increase the rate of solvation since the contact surface area is larger?

Edit: The original question in the book describes dissolving a certain amount of $\ce{NaCl}$ into water and asks, “What can be done to increase the rate of dissolution without affecting solubility?” I assume the rate is measured by how fast the mass of $\ce{NaCl}$ is consumed, which is $-\frac{dW}{dt}$.
If the answers are to be exclusive, then obvious choice is agitating the mixture. 

If the answers are not to be exclusive, then agitating the mixture + increased surface by adding more solute increases $\frac{\mathrm{d}c}{\mathrm{d}t}$

Adding more solute does not increase rate of solvation,  but as the absolute surface increases, it increases $\frac{\mathrm{d}c}{\mathrm{d}t}$.

Note also without affecting solubility from your comment, so increasing temperature is out.