How will be the charged fee increased if use the same account to add one more store

what’s the most cost-effective way to host two or more stores (with different product groups)?

Depends on a lot of factors.

Use the buy-button channel and embed commerce on a second static site/domain can be dirt cheap next to free.

There’s also talking with support and negotiating for a reduced cost multi-store plan.

Note: You used to be able to use the now defunct lite plan for ~$9 for the buy-button channel to put commerce on any website and to also have two separate backends.

Hi,

What will be the cost for having a second site/domain through Shopify?
I’m interested in negotiating for a better pricing for potentially
having 2 or more sites/domains through Shopify. Who should I talk to for
getting a better pricing plan?

When there’s no listed prices/policies for multiple plans a services provides

you have to contact the business support directly to make the attempt and see if they do it.

Buying a domain name (a url) is a separate topic and cost that depends on the domain registrar.