Adding a product without price

My client has different products, some are for sale, others are not, but they’re all on the same page/level, meaning each product still has its own product page, and they also all appear on the same catalog page, if they’re for sale or not.
Of course the products that are not for sale can’t have a price.
I can’t add products that are not for sale in the CMS – as long as I add no price it won’t let me add/save it.

Do I miss something? Can I input something like N/A or dashes or…?
If not, is there a way around that? I’m sure others before me run into that problem.

Thank you!

Here is my site Read-Only: LINK
(how to share your site Read-Only link)

Not sure if this works for your project, but have you tried adding a Switch custom field and then use Conditional Visibility to hide the price and add to cart button from the product page? You can even use the same switch to show content that may be needed on those “not for sale” products that is hidden on the normal products:

I know it’s a bit of a workaround but hopefully it helps out!