no, it is not possible, since you're giving away all control to the remote site.
however, there is a workaround now: you can setup a multi-page form (e.g. 2 forms). the first being the regular form, validated, saved and emails, the second is the "same form" with the alternative action/target URL. Via CSS you can hide all fields (which ontop can be made read-only) in the second form and simply use the success message to indicate: either that information is now sent to a 3rd party site, or to confirm user input etc.