YOOtheme Pro supports the multisite feature in WordPress. You can use YOOtheme Pro for all websites in your network and change the style of each site individually.
Please head over to the official WordPress documentation to learn how to set up a multisite network.
To activate the theme in your network, you first need to install YOOtheme Pro in Network Admin → Themes and enable it network-wide.
Create a child theme for each of your sites in the network where you want to use YOOtheme Pro. The child themes should also be enabled network-wide in Network Admin → Themes.
Open the dashboard of a site in your network and go to Appearance → Themes, activate a child theme and start to configure it. This way each site in the network can have a different style.