@Kate ... depends upon hosting ... and compatibility of Moodle code with PHP version.
Got a VPS? where you are in control of PHP version installed/upgrading PHP?
Then any PHP version higher than what you have but lower than 7.0.x or 7.1 you should be able to run the 2.7's and the 3.2's. There is also changes for DB recommended for 3.3 sites ... which, I'm not sure you should attempt to apply as defaults for DB server due to 2.7's.
See
https://docs.moodle.org/dev/Moodle_3.3_release_notes
and the link to DB requirements
The folowing URL gets you to all the releases where you can check other things:
https://docs.moodle.org/dev/Releases
'spirit of sharing', Ken