He did write about other universes, but none of them were (at least explicitly) about the universes described in Narnia.
I stumbled on this interesting quote from a letter on the Wikipedia article regarding the book's reading order:
I think I agree with your [chronological] order for reading the books more than with your mother's. The series was not planned beforehand as she thinks. When I wrote The Lion I did not know I was going to write any more. Then I wrote P. Caspian as a sequel and still didn't think there would be any more, and when I had done The Voyage I felt quite sure it would be the last, but I found I was wrong. So perhaps it does not matter very much in which order anyone read them. I’m not even sure that all the others were written in the same order in which they were published.
This would suggest that C. S. Lewis didn't know "in advance" how many Narnia books he would write. This would seem to at least open the possibility that he would have written more Narnia books at some point. Even if he had intended to stop writing at 7 books, that isn't necessarily conclusive evidence that he wouldn't have written more. It's certainly not unheard of for authors to continue to add to the canon of their works long after the fact (notably, for example, J. K. Rowling).
The counter to the above argument, of course, is that the original question was whether C. S. Lewis intended to write about the other universes. The fact that he might have written about them doesn't necessarily prove that he actually intended to do so.
With that said, The Magician's Nephew is the only book that even mentions that there are other parallel universes. While The Magician's Nephew was admittedly the second-to-last book, the fact that none of the other books (even The Last Battle, which was written after The Magician's Nephew) even mention it strongly suggests that he didn't particularly intend to write about the other ones. In fact, from a plot perspective, the main reason they visit Charn at all was to bring the White Witch into Narnia. He also kind of needed the Wood between the Worlds to make the plot of Magician's Nephew make sense.
We also have the fact that the magic rings used to reach the Wood Between the Worlds were buried at the end of the book, clearly implying that the characters didn't intend for anyone to use them ever again.
Also, the Narnia series was published at the rate of approximately 1 book a year from 1950 - 1956. C. S. Lewis died in 1963 without writing any more books.
Finally, the Chronicles of Narnia series is the Chronicles of Narnia. The fact that Narnia ended in The Last Battle, and the fact that the series covers Narnia from beginning to end, suggests that he didn't intend to write about any of the others (at least in the Chronicles of Narnia). They fundamentally wouldn't be the chronicles of Narnia at that point, they'd be the chronicles of other universes.
Some C. S. Lewis scholars, most notably Michael Ward in Planet Narnia, have argued that the choice of 7 books was not coincidental. This article in Christianity Today describes that further. To quote from that book:
By the medieval reckoning, there were seven "planets": Jupiter, Mars, the Sun, the Moon, Mercury, Venus, and Saturn. Was it possible, Ward wondered, that each of the seven Narnia books was written under the sign of a different planet? Looking closely at the Narnia Chronicles side-by-side with Lewis' 1935 poem, and other of his writings that touch on the planets, especially his posthumously published book, The Discarded Image, a retrieval of the medieval worldview, Ward found that indeed there is such a correspondence: The Lion, the Witch, and the Wardrobe corresponds to Jupiter, Prince Caspian to Mars, The Voyage of the Dawn Treader to the Sun, The Silver Chair to the Moon, The Horse and His Boy to Mercury, The Magician's Nephew to Venus, and The Last Battle to Saturn.
I'll withhold judgment on whether that theory is true or not, but if it is, that would strongly suggest that C. S. Lewis didn't intend to continue the series.
It seems likely, though, that if he intended to write about other universes, he most likely would've just published them as a separate book (rather than trying to expand the Chronicles of Narnia series, which was always intended to be primarily about Narnia).