What happens if the blood of an animal is transfused to a person?

I remembered a series from Doctor House, where a pig was brought to a patient with a liver failure and both were placed catheters so that they had a joint blood supply system, the pig died safely, and the patient had precious time. I cannot vouch for the reality of such techniques, but I often heard that a person and a pig are very similar in the structure of organs and cells in general.

Such procedures were carried out. This was the beginning of transfusiology. These attempts began in the 17th century, until the 19th century, all of this led to dire consequences and the death of most people. Later, human blood groups were discovered, first three, then another fourth. Then, on top of everything else, the Rh factor. In some cases, people survived when the volume of circulating blood was replenished with the blood of the animal, in some - when they got into the "group", because different animals have different blood compositions, for example, cats have only 3 groups, dogs have about 8 groups. That is, if doctors of the past managed to transfuse blood with a similar immunogenetic composition to a person, then the outcome was not sad. And if on the contrary, there were immunological rejection reactions. Then, a ban was imposed on xenofusiology. For it is necessary to save a person by human methods.