Don't forget embryo selection: if you can create on demand several dozen or hundred eggs, the estimates of gains from embryo selection go from ~0.5 IQ points to 5-10 IQ points (and similarly for any other trait you might want to select for). 0.5 points is pretty trivial and no one will be beating down doors for that; 10 points, however, is a different proposition.
Perhaps more importantly, it's a step towards iterated embryo selection - fertilizing, selecting, then regressing to stem cells, and progressing to sperm/eggs - and doing so for multiple generations, getting +10 points each time, for largely unbounded gains.
We already have the tech to do selection as above but it is cost prohibitive to produce the number of embryos required to do it at scale.
Where you misunderstood was that this is selection, not modification.
We do not know which genes to modify specifically.
We can however, using commonality and statistics, select embryos for increased likelihood of increased intelligence based on a number of different phenotypes.
That's where my understanding ends but the link below has more.
The interesting idea was that we can repeat the selection process using the already selected for embryos - effectively skipping potentially many generations. As in, your kids could more correctly be your great great great great great grandkids.
What I want to know is how far you could theoretically take it before the statistical analysis starts to break down.
As in, can we get to twice as intelligent? Does our statistics / scoring even know what that might look like?
Could we be looking at human induced evolution?
No to your second question; that being the case, your first question has no meaning.
We don't score intelligence with cardinal numbers, which would be required for "twice as intelligent" to make sense as a concept.
We actually do score intelligence with cardinal numbers if one wants to. As I mentioned in my other comment, a number of subtests have absolute scales with true zeros: digit span, vocab, and reaction time come to mind. Quite helpful for cross-species comparisons like humans and chimpanzees...
Or in other words, the fact that one person can be twice as fast as another person in the 100m dash does not make it meaningful to say that one person is twice as athletic as another. In particular, we don't expect the person who is twice as fast to also be twice as flexible or throw the shot-put twice as far, even if those can be made true statements for small (e.g. 5%) difference with appropriate multiplicative factors (e.g., a 5% increase in top-speed predicts a 10% = 2*5% increase in shot-put distance).
It does make it meaningful to say they are twice as fast, though. Which provides a basis for discussing improvements to the general factor. Since there are meaningful zeroes for speed or flexibility or throw distance, it must also be meaningful to discuss doubling the effect of fitness on them. Whether it works out in practice is the question, but it is meaningful and not nonsense.
I feel like something's gotten switched around here. We can measure reaction time with cardinal numbers. Check.
This makes it meaningful to talk about doubling or halving reaction time. Check.
We could attribute part of reaction time performance to the general factor of intelligence. OK... but this will be variable.
It's not obvious to me that if we allot responsibility for someone's reaction time scores among several factors, perform an intervention, get improved reaction times, perform the same allocation, and calculate that the contribution from g has doubled, that we can then conclude that the subject's g has itself doubled.
We want to measure that g has doubled, and we have no numbers for that.
If the effect of fitness on speed is small (as a fraction of absolute speed), then doubling the effect has little to do with doubling speed. If it's large (order unity), then we don't generically expect to be able to double the effect while staying in the regime where intelligence is well defined. These two notions of double are just completely different --
one is a derivative, one is a magnitude -- and it's a mistake to link them.
Of course, there's no way to definitively prove there's any potential to reach above that short of the existence proof of actually creating such people, but there's a lot of considerations which point to much more being possible: many complex traits have been pushed by selective breeding by many SDs, no one has ever been remotely close to genetically optimal and humans are minimally selected for intelligence, there's a large mutation load in terms of gene breakage, absolute measures of cognitive functioning like vocab size or digit span or reaction time generally show humans are nowhere near limits, brain scaling laws do not put humans at near any 0 marginal returns point, etc.
Even if there really is a bound at +100 and being able to increase IQ that much doesn't impress you for some reason, then you can simply spend your selection power on selecting for everything else... I shouldn't need to point out that many other traits are very important aside from intelligence.
Pulling numbers out of a hat here: if we could have even, say, 0.015% of the global population, approximately 1 million people, with an IQ of ~200, the effects on the evolution of knowledge could be staggering.
EX: Garry Kasparov is often said to have a sky high IQ but he tested at 135. He did however have an unusually good memory.
For that, consider the case of distinguished mathematicians who did not score high on IQ like tests.
(To save you the trouble, it's +1.16SD vs +2.51SD; the difference is actually much bigger than it looks because you lose so many embryos in the IVF process, so it's really more like X_1 vs X_196 or +0.56 vs +2.48SD, but to be more precise, you need to go into the weeds of PGSes and per-stage losses in IVF etc. But the order statistics are a good starting point.)