2 installations of wordpress

I have test installation in a separate directory with its own separate database and it works great that way.

I do it all the time to build client’s sites from my hosting. It’s possible by creating a new database and then making a new folder in your public hosting folder. You can put the wordpress files in this new folder.

I did this to test a new theme for my website https://www.christystjohn.com at https://www.christystjohn.com/cstjohn_InterStellar

I have a multisite WP installation

Does the presence of multisite complicate the possibility to have a second WordPress within the same directory tree?

if i make this update a lot of problems do appear,

For what it’s worth, personally I would be inclined to test the new theme under a different domain, completely isolated from the first.

And if you really can’t tolerate disruptions on your production server, you do it like this: https://www.wpbeginner.com/wp-tutorials/how-to-create-staging-environment-for-a-wordpress-site/