Double dose of meloxicam?

I can sympathise with you as I have arthritis in most of my major joints also. As stated above, you can't double your meloxicam, but adding tylenol may help. Tramadol is not a narcotic, but it is a controlled substance, making it one of those drugs Drs are hesitant about prescribing. As with all drugs, it works quite well for some and not at all for others. Unfortunately, I'm one of those others. You might ask your Dr about synvisc injections for your knees. The easy explanation is that they form a layer of cushioning in your knee joint to replace the cartilage that the arthritis is destroying. I found it to be extremely helpful in reducing pain and easing movement. You might also ask about wearing a back and knee braces. Sometimes they'll help provide the extra stability you need for accomplishing daily tasks. Ice and/or heat can help with the pain also. My heating pad is often my best friend! But most importantly is that you must move. Moving is one of the best things you can do for arthritis pain. Yes, even when the pain is excruciating, moving about will help warm and stretch your muscles and actually reduce your pain levels. You should ask your Dr about sending you to physical therapy for a few sessions. They can teach you some gentle stretching and exercises that can also help. I have a couple stretching exercises that I do every morning before getting out of bed that take only a few minutes, but make getting up less painful. I wish you all the best!

No it's not recommended. 15mg is the standard recommended dose. But you can take Tylenol too.
You can also ask your doctor for a stronger anti-inflammatory like a small dose of prednisone per day. 5 or 10 mg in the morning can do wonders for painful joints. Tramadol is narcotic and analgesic, so your doctor may be hesitant to prescribe it.
Have you tried a topical like icy hot or biofreeze? These help also.
Good luck!