My tile setter had to elevate the tiles around the toilet hole in order to make up for some unevennesses. As a result, the toilet flange is approx. 3/8" below the surrounding tile. Can that be compensated for using extra wax ring or will it even be a problem at all?
A double wax ring will probably work but IMO the better option is a toilet flange extender. It is just another flange ring that sits on top of the original flange to get it up to the correct height. Then you install the wax ring and toilet as usual.
I don't have any experience with this particular kit but something like this Toilet Flange Extender Kit.
I have used the Set-Rite Toilet Flange Extender Kits for almost 5 years. They work great. Doubling up wax rings is okay if you want to make your waste line out of wax! These kits have a regular extender toilet flange which will bring your installation to the correct height n top of the finished floor.
Here is how your toilet flange is supposed to look and as you can see all you'll ever need is just one standard wax ring:
They have a couple of videos on YouTube that will help with your install and also have an email & phone support for the DIYer.
Good Luck, but you won't need it with these kits; it's an easy job.
I had a similar situation in my second bathroom, I just used two wax rings. No issues and it's going on about a year now. I've held off calking the toilet down to the tile just to make sure there weren't any "hidden" leaks, you may want to do the same at first just to verify that you have a good strong seal.