Question: When using the Book module, is there any limit on the number of child items that can be added to a book parent node?

Answer: 
Yes, books in Drupal 8 and 9 have a maximum depth of 9, which is the value of the
[`BookManager::BOOK_MAX_DEPTH`](https://api.drupal.org/api/drupal/core%21modules%21book%21src%21BookManager.php/constant/BookManager%3A%3ABOOK_MAX_DEPTH/8.8.x) constant.

```php
const BOOK_MAX_DEPTH = 9;

```
If your question isn't about the hierarchy levels but the number of nodes that can be added in any level here's a question and answer with a lot more information:

[How to increase book weight range for a same-level chapters](https://drupal.stackexchange.com/questions/272952/how-to-increase-book-weight-range-for-a-same-level-chapters)

You can recreate the Book features with Entity reference fields if this is a very serious limitation for you.