Bilingualism is accompanied by biculturalism, and develops the meta-thinking capability.
In general, two different cultures may, or may not, approach the same logical and cognitive environment differently. A perfect bilingual (such as yours truly) or a birth bilingual (such as my daughter) are constantly adjudicating and nuancing the differences between the cultures. A bilingual has to become a judge. Bilingualism is learning two logical systems, and then one is forced to develop the meta-logic to handle them both simultaneously.
So the first thing bilingualism teaches is the relativity of cultures. And how much knowing two languages provides with stereoscopic vision, the ability to perceive a logical dimension, and an emotional dimension, otherwise undetected, and even unsuspected.
I asked, just now, my birth-bilingual seven-year old daughter, about the difference between French and English. She answered, in a cocktail of french and English:”English is poorly pronounced French. But English makes every sentence and word into sing-songs, whereas French is flat. It makes the English more emotional and the French more logical.”
The very fact she used a cocktail for the answer is revealing: she has more words for some nuances in one language relative to the other, depending upon the nuance considered. It clearly augments her mental reach.
The more different the cultures, the more the contrast between the languages, and the mightier the meta-logic to embrace them both.
For example, even though English is mostly poorly pronounced Old French, yet, there are already significant differences in the cultures, and the neurology they lead to. However, European languages are more or less the same: once one knows a few (as I do), one can manage the others. However, when one switches to Chinese, the differences are revealed to be profound. And they extent all the way to mathematics.
Multilingualism is no modern fad. Neolithic people knew generally several languages, because communications were difficult, so particularisms grew fast with distance. Even now in Africa, a few dozens of kilometers away, one can find tonal (most of West Africa), and non-tonal languages (Wolof, Serer). Actually Senegal has dozens of languages, with seven main ones, over a pretty small area. Hence multilingualism is natural: we evolved through it, as a species.
People of culture in Europe, for millennia, knew many languages (at least Latin plus the local language). Charlemagne spoke several languages. Caesar was a birth bilingual (although his last words were in Greek, the language of his first days).
Thus to access higher intelligence, multilingualism may be a deep and strong requirement, ignored all too long.