How about calling the ‘next’ button, ‘submit and continue’ instead (or something less clunky)?
Or have a disclaimer, telling that all partial data is being submitted and used for marketing purposes.
That way you get your consent for every step of the form.
Also think about this: If a visitor enters the name and email but doesn’t want to give away his phone number that’s fine. But if we lose the entire submission because the visitor simply doesn’t want to give the phone number and doesn’t skip but instead abandons the form, we lose everything.
So my point is: I think every field entered and submitted (‘next’ button clicked) is a form of consent anyway and we are allowed to use the data of a partial form submission.
How about leaving that to an A/B-Test?
Yes, you might make certain people a bit more unhappy if you use their data of a partially submitted form. But if it turns out financially more beneficial to your client to use partial submissions then this is the way to go, right? And I’m pretty sure using partial submissions are going to increase the conversion rate down the entire funnel.