In this paper by Bains et al, an alternative to oxygenic photosynthesis is discussed. Apparently, 4 times the amount of biomass can be produced using hydrogenic over oxygenic photosynthesis.
Oxygenic photosynthesis is described by the equation:
$$n\, CO_2 + n\,H_2 O \rightarrow (CH_2 O)\,n + n\, O_2$$ And the hydrogenic process: $$CH_4 + H_2 O \rightarrow CH_2 O + 2H_2$$ Both processes are endothermic, but the bottom one requires only a quarter the sunlight as the one on the top.
This process of interest because, since organisms that use it would have so much expendable energy, it would give rise to a crazy plant world.
As this answer points out, you need some kind of reciprocal metabolism so that the super-plants don't eventually run out of methane and water. In addition to bringing an equilibrium to the planet, I would like this to be a heterotrophic metabolism, so that they can be herbivores that move around and do interesting things.
The only "solution" to this problem that's occurred to me is a metabolism relying on the combustion of hydrogen. But this is stupid because 1) it doesn't address the problem of methane 2) substantial amounts of hydrogen and oxygen in the same atmosphere is a recipe for disaster and 3) even if the combustion process was somehow perfectly contained and no lifeforms ever wanted to develop controlled use of fire, we would have to add another process which renews the oxygen content of the atmosphere.
The answer that I linked does speculate about the possibility of getting enough oxygen from terrestrial carbonate, is this feasible?
If not, what are some ways this could work? I'm open to adding any sort of compound to the atmosphere or crust of the world.