It's to do with emphasis. "The very house" is a stronger, more particular way of saying "the same". "The very same" emphasises the identity even further. This might seem odd, because the same house is either just the same house or it's not. What is intensified through such usage though, is the interest in, or surprise about, or the odds against the house being the same.
the very same/the self-same (=the same person or thing and not a different one - used to emphasize that what you are saying seems
surprising) [American English] We stood in front of the very same
house in which Shakespeare wrote his plays. - Longmans Dictionary of Contemporary English
Though I don't think it's particularly AmE. While we're considering Shakespeare, we might find:
SILENCE This Sir John, cousin, that comes hither anon about soldiers?
SHALLOW The same Sir John, the very same. I see him break
Scoggin’s head at the court gate, when he was a crack not thus high... -
HENRY IV, Act 3 sc 2
How to explain the use of the modifier? It's in the tradition of the "double superlative", which is well-established usage in English. Just as you can't logically have degrees of "the same", you can't have "most unkindest". But many writers (and speakers) have done/do the very same kind of thing to provide the most boldest emphasis.
- "In profane authors there are also many instances of the use of the double superlative. Sir Thomas More used the expression, 'most
basest'; Ben Jonson that of, 'most ancientest'; John Lilly (of the
time of Queen Elizabeth) that of, 'most brightest'; and Shakespeare,
'most boldest, most unkindest, most heaviest.'" ("On the Language of
Uneducated People," - Quoted in About Education - Double Superlative