How can it break it?

Once we came into this agreement of four more decimals, the code would change, but Bitcoin wouldn't break. Satoshi (sat) wouldn't be the base unit (as it is in the source code), but another one which is a thousand times less than that. Transactions signed after this change could have a prefix which would indicate that the user signs based on the new milli-toshi base unit. Any transaction's amount which was signed without this prefix, like the ones before the change, would be considered as a thousand times greater.