Moonshot: "Parameter Scans" with more than two dimensions?

How can we run "Parameter Scans" (i.e. targeting profit optimization or else) with more than two dimensions?
Obviously it wouldn't be possible to visualize with 2d heatmaps or contourplots, however we can probably get a representative idea of the results with APR but ideally with the cumulative return / max drawdown per combination.

I do understand that the computational cost will grow exponentially based on the number of parameters; and I was wondering if this couldn't be speed up using a monte-carlo method.

Thank you for reading.

You can just run the individual backtests, collect the results, then visualize them however you like. There is an example of doing something like this in the pairs trading tutorial.

Yes that would work for me, do you have any pointers on how to use a monte-carlo method to avoid testing all the combinations, but simply to back off early from the ones deemed not relevant?

No I don't. It's not really a QuantRocket-specific question so I would just research general Python solutions.