¡Hola Presto!
To "possible to degrade", the answer is yes - but you supposedly implied "at reasonable cost" or even "economically", and then the answer is unclear. The difficulty is that the most common polymers (PE, PP, PET, PVC, ABS) are very cheap, in the order of 100€/kg, their feedstock even more so, and this leaves very little money for recycling.
Recycling PET into PET (or PE into PE) is possible and done. It makes all the clothes made in Asia of unwoven plastic felt, like gloves and pullovers. Old bottles are sorted out, molten, extruded. With cheap manpower and nearly no transformation, it makes economic sense. If a chemical operation were necessary, it would need to be very cheap.
Fuel: made from polyolefines or old tyres rather than PET if I remember well. Again, the operation is very low-tech, essentially a pyrolysis. While the garbage disappears and less crude oil is used, I wonder if the operation makes our environment really cleaner. The reports don't tell what pollutants the pyrolysis leaves - it could well be a tar with much polycyclic aromatics, much worse than a plastic bottle.
One difficult limit to plastic recycling is that most consumers (...even educated) ignore the composition of a plastic item, so that PE is mixed with PET and even PVC in the garbage. Possibly the most needed progress presently would be a cheap and good machine that sorts out the plastics, either as garbage items or as chips. Which boils down to: identify the polymer quickly enough.
Among the degradation methods, you might consider sunlight, especially UV. But are the products more desirable than the polymers?