The answer to your question is that if both you and your spouse plan to file separately, and you both will need extensions of time to file, then you can (and should) put your spouse's information on a "joint" extension request (Form 4868). You can then both file your tax returns later -- either as Married Filing Separately or as Married Filing Jointly. In other words, no matter how you fill out the extension request (Form 4868), it won't interfere with, or affect, your future discretionary choice on how to file (MFS or MFJ).
If your spouse has already filed their tax return, then you would only need to request an extension for yourself.
Of course, you are both welcome and able to file your separate extension requests as discrete individuals, rather than as a couple. This might be a good choice, for example, if you will be filing as MFS, and you are sending estimated tax payment(s) with your extension requests.
Thank you for asking this important question.
Hi @GeoffreyG do you know where in the IRC is it is mentioned that couples can file 4868 together regardless of filing status?
I know a couple who filed 4868 together, then filed 1040 separately and the 2nd spouse was not considered to have applied for extension, resulting in failure-to-file penalty. She is contesting it but so far no success.
If you are filing separate returns, you will both need to file your own Form 2350. Both the form and the instructions state that if you are filing a JOINT return then you would file a joint 2350, otherwise, you will each file your own.