If you'd like to use multiple RTMP streams, you can accomplish this with OBS using a plugin.
obs-multi-rtmp is a plugin for streaming to multiple RTMP servers concurrently.
This plugin can share encoders with the main output of OBS to save CPU power. It can also use standalone encoders with basic configuration (bitrate).
The current release comes with multiple language translations, and you can find the source code here.
How to Install the Plugin in Windows
1. Download the latest release from https://github.com/sorayuki/obs-multi-rtmp/releases/
2. Unzip the zip file and extract it into the OBS folder located by default in C:\Program Files\obs studio
3. Open the folder path in C:\Program Files\obs studio\data\obs-plugins
4. Complete the installation
How to Install the Plugin in macOS
1. Download the latest release from https://github.com/sorayuki/obs-multi-rtmp/releases/
2. Unzip the zip file and extract it to a location of your choosing
Since you can't extract the file directly in OBS, you'll need to first extract it, then move it into OBS.
3. Once you extracted it, navigate to applications, right-click on OBS, select show package contents, click on contents then plugins, and finally move the extracted folder into the plugins folder
4. Complete the installation
NOTE: Minimum requirements for this plugin are OBS-Studio version 26.1.1 or later, OBS-Studio main unit version built with QT 5.15.2.