You are a major buyer or just a spouse. If you are a buyer. SSN is not a necessary item for you to buy a house. But may affect your loan application. There are loans for people without SSN. But very high rate.
If you are a spouse only, just write an agreement with your apouns to decide how much part are yours and record the agreement (closing agent can help you).
If you are a spouse only, just write an agreement with your apouns to decide how much part are yours and record the agreement (closing agent can help you).