You're going to need a place to put the water once it's filtered, and I don't know anything about your home setup or water requirements, so there are several options that could work for you, or not, depending on your particulars.
If you have a basement or other out of the way storage area where you could have a large reservoir to hold water (a large, thick, plastic garbage can is typically used for 50 gallons or less,) I would put a tee on the outlet from the RO. From the arm of the tee lead to a valve and then to your collection reservoir. Open the valve to add to the reservoir, close it for normal operation. I'm not entirely certain about check valves (or their absence) on the drinking water reservoir and the valve that controls the RO's operation for a drinking water reservoir, so this might not work as I'm thinking. There might be problems with back flow from the pressurized drinking tank or with the valve that controls the system not turning on when you want to fill the reservoir because the tank is already pressurized (if it did have a check valve to prevent back flow.) You could bypass virtually anything with additional tees and valves fairly easily, but each little bit is adding to the cost of the system. Here's a crappy diagram of what I'm thinking.
If you need small amounts of water, 5 gallons or less, you could simply put a bucket in the kitchen sink under the RO tap and open it. Come back in an hour or two and you're set. For more, you could find a tube that fits over the end of the RO faucet and lead it to a larger container. Turn on the tap before bedtime and turn it off in the morning. Once you know the flow through the system and you don't sleep in too long, there's really not much risk of overfilling.