So here's the thing.
Let's say you have an electromagnetic wave of wavelength l, and you send it from where you are to a receiver a distance d away. The total number of cycles of the electromagnetic wave which will fit in that distance is d/l. Using ordinary amplitude modulation, you can therefore fit d/l bits of data in that gap.
If d is something like the diameter of the orbit of Neptune, about 10,000,000,000 kilometres, and l is the wavelength of a typical X-ray, about 1 nanometre, then that number is of the order of ten billion billion bits. Or more! It would depend on how you modulate the signal.
In other words, if you send two probes to roughly opposite ends of the Solar System, and equip one of them with a powerful X-ray laser and the other with a sensitive receiver, you will find that it is possible to fit something like a billion gigabytes in the gap between your two probes. In the ether.
Now the clever bit. Because the information is in transit, there is no reason why the satellites need to have any actual hard storage of their own. If you make it so that each satellite has paired receiver and transmitter, you can program each one to receive the signal, amplify it hugely and transmit it back in the opposite direction, without performing any kind of operation on the signal or storing any part of it (outside of solid-state memory).
You just stored an exabyte of data in hard vacuum using two passive space probes! Neat!
Obviously the complete length of a round trip could be increased just by adding more probes at other points in the solar system. A problem could arise if the signals began to interfere with each other but modifying the frequency slightly for distinct probe pairs would prevent this; each probe would listen on one frequency and transmit on another. This would also allow the probes to duplicate each other's efforts, adding hardware redundancy in case one is destroyed.
The major advantage of this system is that there are no hard drives involved. However, you still need a lot of solid-state processing power and a lot of energy to drive that processing. The probes would need to be located near the Sun, perhaps, to draw solar power, so they couldn't be out by Neptune. This would reduce the distance apart they could be placed. Possibly arrange a few dozen probes in a star-like constellation?