Those attracted to Wittgenstein's later thought like Philosophical Investigations would likely appreciate a lesser known philosopher's thought, that of R. G. Collingwood, too. I'm not alone in finding similarities (not plagiarism) in those two.

A good, short introductory article on Collingwood is here: https://www.prospectmagazine.co.uk/ideas/philosophy/39183/ho...

And a quote from one of his books that reminds me of the private language argument:

" This might seem to presuppose community of language between the speaker and hearer; for unless they were accustomed to use the same words, the hearer in using them to himself would not mean the same thing by them. But community of language is not another situation independent of the situation we have been describing, and prior to it: it is one name by which we refer to that situation itself. One does not first acquire a language and then use it. To possess it and to use it are the same. We only come to possess it by repeatedly and progressively attempting to use it.

"The reader may object that if what is here maintained were true there could never be any absolute assurance, either for the hearer or for the speaker, that the one had understood the other. That is so; but in fact there is no such assurance. The only assurance we possess is an empirical and relative assurance, becoming progressively stronger as conversation proceeds, and based on the fact that neither party seems to the other to be talking nonsense. The question whether they understand each other solvitur interloquendo. If they understand each other well enough to go on talking, they understand each other as well as they need; and there is no better kind of understanding which they can regret not having attained."

I find Collingwood to have more helpful insights for language and communication in general than Wittgenstein, because language as Collingwood explains it includes bodily gestures and, although he doesn't by any means neglect the spoken and written word (which are still important to him), he emphasises the importance of other types of language too. For example, to pull another quote:

"Vocal language is thus only one among many possible languages or orders of languages. Any of these might, by a particular civilization, be developed into a highly organized form of emotional expression. It is sometimes fancied that although any one of these languages might express emotion, vocal language has an exclusive, or at least a pre-eminent, function in the expression of thought. Even if this were true, it would not be of interest at the present stage in our discussion, for we are now dealing with language as it is before being adapted to serve the purposes of thought. As a matter of fact, it is probably not true. There is a story that Buddha once, at the climax of a philosophical discussion, broke into gesture-language as an Oxford philosopher may break into Greek: he took a flower in his hand, and looked at it; one of his disciples smiled, and the master said to him, ‘You have understood me.’"

(Both quotes taken from The Principles of Art, where his main discussion of language is.)