Create a quality profile that extends the default one

I’ve written a custom java plugin with new rules and a new quality profile. The problem is that the new profile only has 1 rule, the one i’ve created.
What i want to do is:

I know that if i want to install my plugin i need Sonar Java plugin first, so after its installation, this adds a quality profile Sonar way. I want my profile to extend this default one, because this is will exists when my plugin gets installed.

Can i do this in code?

Thank you.

Is this feature available while developing a plugin?