Methotrexate (MTX) is a inhibitor of the folic acid pathway, and works by slowing the growth of cells in the body that undergo rapid rates of growth/division. These include immune cells (making the drug immunosupressive), cells of the GI tract, mouth and skin, and malignant (cancer) cells. The direct cellular effects of MTX are unlikely to interact with MDMA in a negative way.
That being said, MTX is hepatotoxic (as mentioned by one of the posters above). Short term use of MTX doesn't cause liver damage, but hepatitis is a side effect in people taking it chronically for inflammatory disorders like rheumatoid arthritis and chron's/colitis. I can't recall the exact incidence of liver toxicity due to MTX, but aprox. 10-15% chance for life long usage is what's coming up in my head.
As mentioned above, MDMA does put a heavy load on the liver, and so taking the two drugs together could cause problems. Hepatotoxicity (i.e. liver damage) isn't absolute however, and depends on a number factors including:
1) How long the person has been on MTX. I know in rheumatological , where 10-25mg/week of MTX is used, liver function is assessed by labs and/or biopsy after a cumulative dose of 1500mg has been taken, and then again every time an additional 1000 mg has been taken. Can you estimate your wife's cumulative dose, and do you know if her liver function has ever been assessed by her doctors?
2) Whether or not your wife is taking a folate supplement. One of the mechanisms of MTX liver toxicty is depletion of hepatic folate stores. Folic acid 5mg/week or folinic acid 2.5mg/week reduces the risk of hepatoxicity. If she hasn't been on a folate supplement, I'd recommend not taking the MTX.
3) Whether or not your wife has other risk factors for liver damage including frequent use of alcohol or other hepatotoxic drugs like acetaminophen, obesity, infection with a hepatitis virus, etc.
*disclaimer*: The above post is simple medical theory and should not be taken as medical advice for your wife