The witches brew in the streets of NO there is no way you could purify it. It just has too many diffrent mixes for any one or even several methods to work.

Distilling would be best to remove disolved solids. Salt or other like chemical cpompounds. Also any bio contamination. As they can be treated as solids. But volitile liquids such as patrolium would go along for the ride. It you had the wherewithall to set up fractional distillation some of thes would be removed.

Then you would have to run it through a charcoal filter. This might remove most of the volitile contamination. Patrolium being the worst.

Then a reverse osmosis filter to clean it further.

Then maybe a second seperate charcoal filter.

You might end up with something drinkable. But and its a big one fith some of the stuff mixed in fromm chemical plants and even household chemicals the chance are still far too great that it might still be a leathal drink. I would not trust it.