Is there any evidence of malleability of fluid intelligence?
In the downward direction, definitely yes.
There are many ways you can directly pull fluid intelligence downwards. Things like being exposed to much lead, suffering from iodine deficiency (especially a developing fetus during pregnancy, see e.g. (Qian et al, 2005)), or by not getting decent nutrition. Anything that interferes with a healthy development of the brain might be implicated in intelligence. Similarly, you could presumably push intelligence downward by directly harming the brain (Brain lesions, anyone?). Fluid intelligence also lowers with ageing (Whitley et al, 2016), and so anything that slows down the ageing process may also have an effect.
Next, let's consider the more interesting question:
Besides avoiding decreases in fluid intelligence, can we push it up?
There does not seem to be a reliable way of increasing intelligence known (as of yet), perhaps except for one.
Here we have to turn to Richard Haier, the editor-in-chief of the journal Intelligence, as he has written extensively on this topic. Perhaps disappointingly, we refer to his article Increased Intelligence is a Myth (So Far). The title says it all. He goes into details with the difficulties of establishing increased intelligence. You need to show that you're not just raising test scores, but actually something that transfers over to general intelligence. He also goes into further detail regarding the topic of increasing intelligence in his book The Neuroscience of Intelligence.
To truly appreciate the difficulty of increasing intelligence, you really need to understand the history of methods being suggested. This also helps you develop a healthy amount of scepticism -- you should not believe any method without a substantial amount of evidence backing it up. What has been suggested to increase intelligence? First, the Mozart effect. Meta-analyses show no convincing effect especially when you consider the evidence of publication bias (Pietschnig et al, 2010). The second craze was memory training as you've already noted. Again, not convincing (Melby-Lervåg et al, 2016). Similarly, chess training has been suggested as a way of improving intelligence, but the results are not great (Sala & Gobet, 2017). Now the craze is video games, although it suffers from many of the same methodological issues: (very) small sample sizes, and probably publication bias.
While people can cite all kinds of studies showing increases in intelligence, the real question is really whether these can withstand hard scientific scrutiny.
It is likely not impossible to raise intelligence. Haier suggests some plausible ways of increasing intelligence in his book, but no massive evidence yet. Currently there does not seem to be a very convincing way of increasing intelligence...
...Perhaps except for one way?
Education has been suggested as a candidate for improving intelligence. There is a question whether education really increases general intelligence or just specific skills (Ritchie, Bates, Deary, 2015), but currently education is the best bet (Ritchie & Tucker-Drob, Preprint 2017). Ritchie and Tucker-Drob report the following:
Education appears to be the most consistent, robust, and durable method yet to be identified for raising intelligence.
However, even here we should withhold some scepticism. First, it may simply be increases of specific skills. Secondly, the fadeout effect is pervasive in psychological research of intelligence. Intelligence increases do not seem to last. For example, massive programs such as Head Start showed some initial increases in intelligence measurements, but this boost eventually fades out (Protzko, 2015).
Like Head Start, other programs have been created with the purpose of increasing school performance. For example, the Bill & Melinda Gates Foundation program Gates Effective Teaching Initiative did not see the benefits it hoped.
It might also be hypothesized that expensive private schools would improve the intelligence of the pupils (beyond regular schools). It is well known that pupils of these private schools show higher average scores, but the question is: is it because of the schools? These schools are also highly selective; the pupils attending these expensive private schools are not representative of the general population. This has been tested in at least one large sample. They found that after controlling for factors involved in prior pupil selection, there remained no statistical difference (Smith-Woolley,..., Kovas, Plomin, 2018). In other words, they found that expensive private schools did not demonstrate improvements in intelligence beyond what ordinary schools did.
In fact, all of this goes back to Arthur Jensen's infamous 1969 paper How Much Can We Boost IQ and Scholastic Achievement, which made intelligence research controversial if it wasn't already. He concluded already back then that teaching intervention did not show noticeable improvements. Jensen's opening line in his long paper:
Compensatory education has been tried and it apparently has failed.
So currently, if education can increase intelligence it does not appear to be through teaching intervention, but simply through longer education.
Summary
- Many methods for increasing intelligence have been suggested. They tend to not withstand proper scientific scrutiny.
- Therefore, it is important to have some healthy scepticism to suggested methods, and accept them only when a high evidential threshold has been reached.
- Currently, the most backed up way of increasing intelligence is through longer education. However, even here it is not certain, and more research is needed to understand the relationship between education and intelligence.