If you can convince the world's governments to randomly vary carbon emissions from 20% to 140% of the current, for periods of a decade at a time, then we can collect a great data set. Anything less than roughly that variation, over roughly that timescale, isn't predicted to make the climate change enough to detect given the expected accuracy of our currrent models. No point doing an experiment that won't even test our models.

Otherwise, we're limited to n=1, exactly what we've got, for the climate as a whole, and experiments need to be done to understand the physical processes at play and whether we have the details right enough.