Yes... yay! :)
But with some conditions:
We're reasonable and understand that you probably have one or more home computers, a laptop and probably one at work too. You may also have both Windows and macOS computers. Using a single license across multiple computers AND operating systems is OK. Provided ..
You are the only person using FL Studio, the plugin or whatever software you purchased. The best way to ensure this is to install FL Studio for your personal account (not 'All users'). So yes, multiple installations are OK, where you are the only user.
This option is not applicable to companies, organizations or schools, they need to purchase a multiple license version.
To remove a license from a computer:
See the this Knowledge Base article - Removing Licenses.
WARNING ABOUT ABUSE
Be aware that abuse of this privilege will not be tolerated. Where we detect more than one person using the same license, your Software license can be revoked and account deactivated (see our End User License Agreement).
Not only do we prohibit you sharing your FL Studio activation with friends, it is a particularly bad idea, since you can't control who they pass it onto. Think seriously, best friends, have other best friends, and you may not always be best friends with your best friend. Once your license is 'out there' it will spread, quickly. We have seen cases of a license ending up on the internet within weeks and 10,000's attempted installations after we shut an account down.
Different versions of FL Studio:
FL Studio Windows 32 & 64 bit - You can install both of these versions using the same registration on all your computers, under the conditions listed above.
FL Studio for macOS - This program can be installed on all your Mac computers, under the same conditions listed above.
Image-Line Support Team