An unreasonably effective technique: plot many graphs of different dimensions.
Humans are very good at noticing patterns.
Data often contains huge numbers of insights, but they are lost amongst the noise.
Often the dimensions that are most predictive are not obvious ahead of time.
If you generate tons and tons of graphs of different dimensions plotted against each other, you can skim through quickly and find the most interesting ones.
Don't try to guess ahead of time which combinations are most powerful.
Discover the most powerful ones and then unpack why they are most interesting.