In the phrase:
"Иван" is in the genitive, which means that the above translates to "Ivan's house". Following this pattern, if I wanted to say "my house", I should logically be able to do that by using я in the genitive:
However, in practice I always hear it as "мой дом". Is it ever possible to use "дом меня" to mean "my house"? If so, how is it different to "мой дом"?