Any sales without fair market value is un-enforceble. If the seller accept your suggestion. He can sue you later and ask you pay the different between you pay on table (much less than fair market value) and the fair market value. If you admit already paid him cash or other consideration, you both admit cheating /fraud to state to pay less tax.
The unfair transaction can only happen between family member. say father give a house to daughter.
If the seller sign a contract to sell the house to you for 1 cent. He can get the house back later with out any bay back. If he sell a house to you for $500k (if the house can worth $600k. The realtor will ask to stop the sell and re list the property for $500k, that may bring many offers. If the seller do not agree, the Realtor may ask full commisssion based on original listing price.
Real estate transaction is very complex and a good agent/broker need a lot knowledge. People with your knowledge do transaction with out professional help take great risk.