NPR has an article about the measles. It is already known that after a measles infection the immune system goes down for a few weeks and followup infections are common. It seems that what the infection does is worse than that. With the introduction of measles vaccination it has been observed that other infections went down within 2-3 years after measles immunization took place. Researchers wanted to know why and found evidence that
Like many viruses, measles is known to suppress the immune system for a few weeks after an infection. But previous studies in monkeys have suggested that measles takes this suppression to a whole new level: It erases immune protection to other diseases, Mina says. So what does that mean? Well, say you get the chicken pox when you’re 4 years old. Your immune system figures out how to fight it. So you don’t get it again. But if you get measles when you’re 5 years old, it could wipe out the memory of how to beat back the chicken pox. It’s like the immune system has amnesia, Mina says.
So parents putting their children into a “measles party” in order for them to “gain natural immunzation” may actually achieve the exact opposite of that.