IQ tests were not developed to measure the high end, and have never done this very well. They were designed to find children in school who need extra help.
They also were not designed to measure the intelligence of adults.
IQ is a ratio of chronological age to the “age” of academic achievement. As such, adults don’t really have an IQ. When you hear adults tell you they have an IQ of whatever, it’s usually the last tested IQ they had in school, which was probably from before they were in high school.
The highest upward measure of most IQ tests used in schools is 150. Anyone who scores above this is simply labeled “above testing parameters.” That’s why it’s such a joke when TV geniuses say they have an IQ of something like “187.” Especially if they are adults.
Yes, some people have an extrapolated IQ, and if you pay a psychologist a lot of money, you can get an IQ test at any age, and yes, Mensa has some kind of test they give potential members, but those are all extrapolated IQs.
Yes, you can increase your IQ.
You can always increase your ability to perform on an IQ test, and that is how an IQ is measured. IQ tests problem-solving skills, memory, general knowledge, and reading ability (as a discrete skill), in order to predict performance in a school environment. You can always improve your ability to achieve in school, no matter how old you are, so yes, you can increase your IQ.
Is there some quality called “intelligence” separate from achievement? Maybe. Can we measure it? We try. There is a lot of research and effort put into trying to measure it in people on the lower end of the scale, to determine what sorts of interventions are needed. There is a lot at stake in developing a good prognosis for someone who is developmentally disabled.
But for someone on the high achieving end, IQ is mostly a curiosity. Once a person is “above average,” and not needing any special help at all, there’s no need to measure IQ. Actual performance is more important in determining things like placement in accelerated programs.
Just as a side note, a lot of people who were middling achievers in school before the 21st century, and later diagnosed with AD[H]D or anxiety disorders (sometimes as part of autism, sometimes not), and either given medication, or behavior therapy, or both, have attempted college again after failing once, and found it a breeze. No doubt they would have scored much higher on IQ tests if they’d had intervention the first time around.
So yes, there are ways to increase IQ. Lots of them.
ETA: full disclosure: my last tested IQ was in the 7th grade, and it was 142. That’s phenomenal. I never lived up to it. However, in college, as part of a psych experiment I volunteered for, I took a multiple choice test, the purpose of which was to measure one’s ability to take multiple choice tests. I scored a 98%. The next highest score was 76%. So I do not think IQ tests measure anything but one’s ability to take an IQ test.