One way to extrapolate: excess deaths. Look at the overall death rate for an area and compare it to the normal value when there isn't an epidemic going on. If there is a difference that is larger than your number of known Covid deaths (which is true for Italy by a factor of somewhere between 2x and 5x), you can assume you're undercounting your Covid deaths by that factor, and your overall Covid infections by at least that factor.
This still involves guesswork wrt the ratio of deaths to infections (IFR). Proper statistical sampling is the only way to get an actual answer.
The usefulness of that approach decreases as people's behavior otherwise changes. For example, accidents account for ~10% of deaths. It's quite feasible (and I think we already have data to support this) that that has dropped a lot due to people's behavior changing in response to covid-19.
Forget accidents, there’s a dropoff in heart attack, stroke, and cancer deaths as every death now is attributed to Coronavirus.
It is unknown what percentage of people who are infected get symptoms and it is largely unknown what percentage of people who get symptoms ultimately die. So there is no way to calculate anything.
It's just a lower accuracy level of estimate, not an invalid method. For example you can know that an infected person that had no known contact with another infected person means that there is in fact at least one other infected person out there. Yes, not as accurate as random population testing, but it's a difference of degree, not kind.