Mine are 11 and 9, and I tutored my own dd to pass the 11+ with a 90%+pass rate. However, it's worth dissociating 11+ vs what I think you'd rather and that is intelligence and learning.
First on my list is TRAVEL. I know it's super expensive and is a luxury. My kids will never forget Botera having seen his works near Bogata, Columbia. Will remember Hans Christian Andersen's hometown and life story in Denmark. Know how Isaac Newton discovered splitting light in his bedroom in Woolthorpe.
There's reading and there's reading comprehension. The latter is harder work on the parent. Are you going through vocab, alternative vocab, context, recall as well as prediction on what's going to happen next in the story? Do you get them to use a dictionary? Do you get them to write unknown words down and then you revisit these same words in your own conversations with your kids? You could read just 2 pages together but spend 10/15 minutes going through comprehension, without the need to fast forward anymore in the story and it's this that makes a massive difference to learning. Obviously not all the time as you'd want to get on with the story but having had a long conversation with a SEN specialist (friend of mine), I have completed changed the way I read with my kids and the difference is remarkable, especially for my youngest who's a boy and has always struggled. Within 9months, he went from middle to bottom set to now top set in English.
I focus hugely on mental maths, conversions, that kind of thing but I'm confident with Maths having studied it at Uni. However, there's loads on YouTube so you don't really need to be an expert needs these days!
Coding like Scratch and back to maths, multi-step maths questions helps.
For me, it's not so much quantity but quality. It's about stretch and sometimes being outside the comfort zone and introducing topics from sources of material such as National Geographic, First News, watching documentaries like Cosmos: Space Time Odessy and visiting places like Bletchley Park.
Every Sunday morning breakfast time, we all sit reading broadsheet newspapers in the lounge. Even mine as young as 8 started to read excerpts of the Times/Independent. They weren't able to understand it all but as it was relevant and newsworthy, we could then follow-up on YouTube or the Sky News to learn more.
I think, in my own personal opinion, what needs to be encouraged is a thirst and enjoyment for learning and building that cultural capita as well as building foundational building. I have a Masters degree in Chemistry and work alongside some pretty genius people at work (one of the founding fathers of an internet protocol, inventors with their own ip, NASA people) so I'm always quizzing them on how they raise their kids. LOL.