If you do mechanical recycling, for instance, you would not break down the molecular structure of the plastic. You would recycle the molecular structure as such, which would consume less energy, so yes, you can recycle it many times again.
If you do chemical recycling, it's more energy-intensive. You would basically break down the molecular structure to monomers. Those monomers can be reused. The advantage of that is that the purity of the plastic you recycle will be higher, but it's more energy-intensive in that sense.
Still, any recycling type would be much more interesting than, for example, incinerating or disposing of the waste in landfills.