How can I upgrade the Android version if the manufacturer has stopped doing it?

Officially, neither as and without "dancing with a tambourine", if the manufacturer has abandoned the update or for some reason to upgrade the android version to a specific model. And so look in the specialized forums where there are good custom firmwares for the version of android you need, if someone decided to make one.

The number of customizations depends on the popularity of the smartphone model and the desire of users to install and test them.

I subscribe to the opinion of the previous author Mr. Ice. I just want to add that when installing a custom (unofficial) firmware, you must be prepared for what you can:
1. Don't get what you want;
2. Get more problems than fun;
3. With a small mistake, when flashing, or filling a defective / incomplete image into the phone, get a brick.
4. Loss of the guarantee if it has not expired yet.
... etc. etc.
Everything, in short, at your own peril and risk.
Although, it is possible that everything will be fine.
Good luck and patience to you!