Developing/extending a live site?

Hello everyone.
Can some of you please share his experience on best techniques of development/extending a live WP site ?

I am having a customer who is sending tons of requests each day and they are not only design related, but also function related, meaning I need to install and test new plugins.

Now, I know I can download the live site database locally (I’m working on a lampp platform where https://sitename.tld is local version of https://WWW.sitename.tld) and upload the new code and database once I am finished, but the problem is that the web page is getting constantly updated since its for a news publishing company.

Is there a technique I can use so I won’t have to install the desired plugin twice: first locally, test it and then install it again on the live web page? Seems like a waste of time.