Since an answer with "What's more" has not yet been put forward, here's one.
"What's more" would be a pretty good equivalent because it carries the sense that the thing added goes beyond whatever came before. Here's a typical use.
In the 1939 film adaptation of The Hunchback of Notre Dame, the character of Jehan Frollo is no longer a sixteen-year-old troublemaker but a judge. What's more, he assumes most of the traits his brother Claude possesses in the book, and effectively usurps that character's role in the plot.
On the other hand, "furthermore" is better suited to elaborating on an idea or pursuing an argument, and not necessarily by adding something stronger than the previous point.
Whether Hugo's claim that some of the chapters inserted in the later edition of Notre-Dame de Paris were in fact recovered originals is doubtful given their slight but noticeable difference in style. Furthermore, the excuse he gives for not including any of the other chapters he claims to have lost during the original composition of the novel is questionable: he states that he simply did not have the inclination to rewrite them after losing them and so moved on.
— N.B. I don't know whether scholars actually doubt the claim. Just trying to use "furthermore".
According to this translation memory website, other human translations of "Il y a plus" include:
There is more.
That is not all.
It goes beyond that.
There is more to it than that.
Which exactly is the best translation for the NDdP sentence depends on the wider context and style. Among those, I think the best alternative here might be "That's not all".