Does the amount of solute affect rate of solvation?
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.