If it's cloudy it's cloudy, there is less sun, and if there is less sun to harvest then photovoltaic panels will produce less. We can maybe optimize the panels for cloudy days but whatever happen they will always produce less energy in cloudy days than sunny days.

So there is multiple alternatives:

• Adapt electric consomption to the weather. I think this is a really important step. With technology we progressively disconnected ourself from the weather. Whatever season it is, whatever the outside temperature we always go to school/work at the same hours, eat the same kind of meals at the same time ... I think with renewables we have to think differently, of we have a sunny day we can do laundry, stay up late, use the electric oven ... In cloudy days we reduce our use of electricity.
• Storage, storage is good for predictable energy variation, maybe to extend a bag day but not more. Whatever amount of storage we install we will still have days when it's not enough, the worst case scenario
• Alternative energy, for when there is no production and the storage is empty then we need to rely on alternative energy. It can be an alternative generator, individual or collective, or it can be having wood stove for cooking and heading and candle for the light. This will cover the x% of hours in the year when we run out.

When I was living on a sailboat, the logic of overcast days was this; that overcast days are often stormy days, so have a wind generator for the "bad weather". But this may not work in your place - sometimes it is just a low-energy day; cloudy and calm.

Of course the other approach is storage; but it tends to be expensive.