How to work online on a WP page for a client

Hi guys,

I was wondering what is the best way to build a website for a client but on your own server without buying a domain.

My client wants to look how the site will be build but he got his own site now and want to keep this online till the new site is online.

the best thing would be to build his site on a own part of my site like:

https://www.myownsite.com/siteofclient

But it looks this wouldnt be possible cause you have a conflict with more themes then? What is the best solution to do this?

Thanx!