This worked for me when I wanted to allow an employee to use my inhouse-developed inventory software that runs on the business's MacPro (macOS HighSierra 10.13.4) using MAMP free (4.2.1):
Be sure to stop MAMP servers and close the app before doing these steps.
1) Create a user/group account to use for running MAMP. For directions, go to https://support.apple.com/kb/PH25796
2) Install MAMP using this user/group OR (if already installed) change the owner/group of the MAMP files to this new user group. From Terminal:
sudo chown -R MAMPuser /Applications/MAMP
sudo chgrp -R MAMPgroup /Applications/MAMP
3) Change permissions on all the MAMP folders/files to let group members read, write and execute. (NOTE: This is for convenience, not security; investigate the implications of this if you are worried about other users messing up your install.) From Terminal:
sudo chmod -R g+rwx /Applications/MAMP
Of particular importance were the mysql database folders /Applications/MAMP/db/mysql56, so if you have issues starting MySQL server, double check the permissions on the items in that folder.
4) Change the permissions on your Apache Document Root folder as appropriate to allow your php website to run for members of MAMPgroup.
(NOTE: Again, this is for convenience, not security; investigate the implications of this if you are worried about other users messing up your website.)
sudo chmod -R g+rwx <path-to-document-root>
5) Add user accounts that you want to be able to run MAMP to the MAMPgroup. For directions, go to https://support.apple.com/kb/PH25796
6) For each user, set up an Automator application with the following Utilities -> Run Shell Script command:
sudo -u MAMPuser /Applications/MAMP/MAMP.app/Contents/MacOS/MAMP >/dev/null 2>&1 &
This runs the graphical MAMP app from the MAMPuser account no matter who is logged in.
For information on how to use Automator, check out https://developer.apple.com/library/content/documentation/AppleApplications/Conceptual/AutomatorConcepts/Automator.html
Make sure that users know to stop the servers and exit the MAMP app before they log out.
NOTE: It is possible to just create a group for any users who need access to MAMP. However, when a different user starts MAMP, a "MAMP wants to make changes. Enter admin name/pswd" pop-up appears. This solution runs the app under the same user account (sudo -u MAMPuser). There are glitches if MAMP is already running, so be sure that users always stop servers and exit MAMP when they are done.