Can I sign my emails with both S/MIME and PGP/GPG?

Question

And if it possible, is there any benefit from doing so in one order or the other?

signWithSMIME(signWithPGP(message))

versus

signWithPGP(signWithSMIME(message))

Also, are there any reason not to sign with both?

Answer 1

Although I do not really see the benefit, in principle it possible using the first approach if you sign first with PGP/INLINE (aka PGP traditional). The second option will not work since signing with PGP after signing with S/MIME will break the S/MIME message, i.e., the S/MIME message will no longer be a valid S/MIME message.