Yes it is very possible but you will need 2 databases, or else changes to one will effect another.

It will be treated like a separate site in the sub directory.

Absolutely possible. Just upload the files twice. One in each directory you want and create 2 databases.

It will depend..

- First take a backup of your existing website database and files.

1 ] If both the templates are from the same framework/technology, it is easy and less time consuming. e.g. In case of Wordpress, simply activate another theme (ideally visit WP dashboard -> Appearance -> Customize) to see how will your store look like.

2] If the template that you want to test has been developed/belong to some another framework/technology then you will do the following:

- Install it in the subdirectory of your main website directory

In this scenario, you will need to have a separate database. (2 databases, one is already there that belongs to your existing website and another database will hold the data of your new template to test the things out).

This is because if you have a Wordpress site and another template is a Joomla template (to be tested) then you should have a separate database.

3] If you are using Wordpress, research the concept of "Wordpress Multisite" to see how it can benefit you.

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thank you guys. you are really helpful.
Far Next - I do not use a wordpress, I want to install a prestashop.

domain is not limited, but two databases are needed

If you would like to have a completely different store/template on www.mysite.com/shop then just create a new folder in your websites main directory and name it shop. Then just upload the secondary template into that folder.