You can run a water reactor with a much faster spectrum if you have more fuel and less water.
Shippingport was able to breed on the Thorium-U233 cycle.
Plutonium breeding could also be accomplished with a water reactor, possibly with two separate reactors in the fuel cycle to tune up the use of odd and even numbered isotopes. See
The trouble with it is that water has limited ability to remove heat so you are going to have a large amount of fuel tied up creating a critical mass producing relatively little water. That makes it hard to build up the fuel inventory for a fleet of breeders and economics are even worse than today's water reactors.
Shippingport was able to breed on the Thorium-U233 cycle.
Plutonium breeding could also be accomplished with a water reactor, possibly with two separate reactors in the fuel cycle to tune up the use of odd and even numbered isotopes. See
https://en.wikipedia.org/wiki/Supercritical_water_reactor
The trouble with it is that water has limited ability to remove heat so you are going to have a large amount of fuel tied up creating a critical mass producing relatively little water. That makes it hard to build up the fuel inventory for a fleet of breeders and economics are even worse than today's water reactors.