positive externalities are charities, or non-profits at least.
There are zero private businesses which generate positive externalities that they do not charge money for (and if they did, then it's no longer an externality). To do so would mean they leave money on the table! They can only shed negative externalities.
> To do so would mean they leave money on the table!
Generally it means that they can't capture the full value they add.
If I have a business installing domestic solar panels, I can capture the economic benefit to a homeowner of getting cheaper electricity, but not the broader impact of helping to decarbonise the grid.
(There might be a subsidy for this business where you live, but that's irrelevant: in principle a business like this can exist and be profitable without capturing all of the value it creates).
I’d suggest cafe seating as a positive externality. The people eating are paying for the food, and table. But passersby and neighbors are gaining eyes on the street, the prospective social interactions, etc. The foot traffic might also be enough for another small business to consider open, and thus begin maintaining the store front and street. These things have utility to people who are not paying to eat or drink at the cafe.
A trade takes place when both buyer and seller feels they gain something from the transaction. In general neither side captures all the surplus value, if they did the trade would not happen.
There are zero private businesses which generate positive externalities that they do not charge money for (and if they did, then it's no longer an externality). To do so would mean they leave money on the table! They can only shed negative externalities.