You can amend from MFS to MFJ at any time (you can't amend the other way around). If any refund is due, it won't be paid for any tax return earlier than 2016, because there is a 3 year deadline on getting refunds from amended returns. (The deadline to amend 2015 was April 15, 2019, three years after the original filing deadline of April 15, 2016.)
When filing jointly, you must report and pay US income tax on all the world-wide income for both you and your spouse. There is an offsetting tax credit for taxes paid in a foreign country, but you would need to test to see if your spouse's income results in more tax than you save by filing jointly.
Also, if filing jointly would make you eligible for Earned Income Credit or the Additional Child Tax Credit, those credits will not be paid, since your spouse would have to have their ITIN issued before the deadline of an on-time tax return for that year. Since the ITIN won't be issued until after April 15, 2019, you won't be eligible for EIC or ACTC on an amended 2016 or 2017 return. You would only be eligible on your 2018 return if you filed a request for an extension before April 15 (which makes a return filed in May or June an "on-time" return).
You will need to apply for the ITIN by filing a joint return now and mailing it to the IRS along with the W-7 ITIN application and required proofs. In most cases, the IRS will not process an ITIN request unless it is attached to a tax return. See more below.
If you are a US taxpayer (citizen or resident alien) married to a non-resident alien you have two choices.
You can file as married filing separately. You do not list your spouse as a dependent. Leave the spouse's SSN blank. You can't e-file. Print your return, write "NRA" for the spouse's SSN, and mail in your return. Married filing separately has the highest tax rates and many deductions and credits are reduced or disallowed.
Or, you can make an election to treat your spouse as a US person for tax reasons, in which case you can file as married filing jointly. Treating your spouse as a US person means you must report and pay US income tax on their income from anywhere in the world (there is an offsetting credit for foreign taxes). You get lower tax rates and some other benefits by filing jointly, but the worldwide tax thing might cost you more than you save. Your spouse needs an ITIN (international tax ID number). If you have it, you can e-file the MFJ return. If your spouse does not yet have an ITIN, you can't e-file. You need to print your return and mail it to the IRS, along with a form W-7 ITIN application and any required proofs. You will need a fake SSN to get through the interview, try 999-88-9999. After printing the return, cover the fake SSN with white-out. Mail your return and form W-7 to the address in the W-7 instructions, not the usual address for your tax return.
You won't be able to file your state tax return at this time. Once the IRS sends you back a letter with your spouse's ITIN, add that to your tax return and then print, sign and mail your state tax return.
https://www.irs.gov/uac/about-form-w7
https://www.irs.gov/individuals/international-taxpayers/nonresident-spouse-treated-as-a-resident
