There is a long list of supplements that can possibly help with depression, the problem is going through the process of sampling them all till you find one that might work. And some, like the one mentioned above can sometimes cost more. SAM-e dosage that is needed for some can be 8 gram and can be expensive. Then you have St. John's Wart, 5-HTP, Saffron extract, Ginseng, Fish Oil, Vitamin D (if deficient), Rhodiola, Goat's Rue, and a dozen more. Pay attention to factors like if the it is enteric coated, if it is full spectrum versus an extract and if an extract which active ingredients are being used (Some have multiple active ingredients and which one may determine if it is effective for you). I hate to complicate it but that is the real world reality. Then you have exercise, intimacy, hobbies and a slew of other activities that can greatly help with depression, depending on the person.
Everything depends on you and all your variables. Do keep in mind that some supplements affect other things in the body. Some will affect hormone levels, like estrogen, absorption of other nutrients and medications, can affect the effectiveness of certain birth control methods and so forth. Mixing supplements with other drugs can be detrimental if you do not research first, like Berberine some use as a replacement for metformin, can make some drugs far more potent causing major issues. The negatives are rarely discuss as everyone wants to find the magic cure all. So, be careful and read up on anything you try to find out what the possible downsides are, they are shamefully hard to dig up. The benefit of the doctor is whatever drug he prescribes, he should take into consideration a lot of the above.
Best wishes and hope it works out for you.