You need to consult with an immigration attorney regarding your options. The fact that you have 2 years left on your visa does not, in any way, affect how long you can stay here. The document that dictates how long you can stay is the white I-94 card you received at the airport. While it is technically possible to apply to extend one's stay beyond the date stamped on the I-94, the application also requires proof that you only intend to remain here temporarily and then return to your country. If your intention is to remain here permanently, applying for an extension of tourist status may be problematic.
I think you should seriously consider talking your fiancee for a consultation with an immigration attorney.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: email@example.com; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.
This sort of question requires careful counseling so that you can make the best decision based upon your situation. We do not know all of the facts. In general, a person is only allowed to extend a visitor visa if they have non-immigrant intent. This is not the case. Therefore, you should not take any further action without a more intensive discussion of all your visa options. Good luck.
This is general information, not legal advice, and does not create an attorney client relationship.