So conceptually, if a capacitor is connected to a voltage source, and if you decrease the distance between two plates, the electric field in between the plates increases. This means that you can hold more charge on each plate because there's more force there now, increasing the capacitance. So it seems like a stronger electric field between plates will lead to a higher capacitance, but then dielectrics increase capacitance by decreasing the electric field.
If the electric field is decreased, won't the plates be able to hold less charge?
The only way I could reason it would be that by decreasing the effective electric field, you are decreasing the voltage and if you are connected to a voltage source, you would need to maintain that constant voltage, so you would have to increase the amount of charge you hold in order to get back to that constant voltage. By increasing the amount of charge you hold, don't you also increase the electric field again so your effective electric field will end being the same as without the dielectric?