Ok, this is a great example as to why it's better to just give your entire scenario with all your requirements instead of asking how to do one thing, in my opinion. I've gleaned from your 2nd post that we don't need separate forms necessarily, but you do need separate views while maintaining some of the same data. It's better to let us help you find the best approach based on your requirements as opposed to going down a path you come up with on your own without knowing all the capabilities of InfoPath. It's a very powerful tool that can do many things to streamline your needs. Here are my suggestions.
1) Do the users REALLY have to sign it physically? Isn't it better to have electronic or even digital signatures? Infopath gives you this option, and it's far better than printing, mailing, signing, and mailing again. That is terribly inefficient, and people have far better things to do than waste a lot of time with that old, manual process. I would think a large company has invested in technology that helps streamline such things. Hand-written signatures are a thing of the past. If your company hasn't invested in such technology, then show them they have it by working it in InfoPath. You can choose the Submit to Email option so that when you're done with filling out the form, you can click submit, and it will automatically go to people you pre-define as well as the person who the form is for. That way, everyone sees it, and either the person can sign it electronically (or digitally) in the email, or the person can print it, sign it, and mail/scan/email it back. That's still way better than you printing and mailing.
2) If you have 3 different forms that share a lot of the same data, then perhaps try creating 3 separate views with different formatting, layout, design, etc., but use the same data fields. That way, when the first view is filled out, you can print it, but you keep the form open. You then switch to the next view using the view selector (or by adding a button with a rule that switches views), and then all the data that you've already filled out is still available for the next view, which represents your next form. This form can look completely different, but it shares the same form template and data fields. Likewise for your 3rd form/view.