Not sure, but I think Hangul counts as a second invention of alphabetic writing.
If you count syllabic writing systems (which are not technically alphabetic, but are more so than Chinese, or Mayan or Egyptian hieroglyphics), there are more: Japanese hiragana and katakana, Cherokee syllabics, Pahawh Hmong, Vai (West Africa), and Linear B (and presumably Linear A).
There's also Thaana, the script used for Maldivian, which uses some Arabic script symbols, as well as Indic digits. So while it's semi-alphabetic (partly abugida), and it's derived from existing writing systems, it uses the borrowed symbols in unique ways.
There are other syllabic writing systems as well, like Inuktitut and Cree, but those were created by missionaries familiar with other writing systems.
> Not sure, but I think Hangul counts as a second invention of alphabetic writing.
It is my understanding that Hangul is believed to have been influenced by other alphabetic writing (e.g. Phagspa) which themselves descended from the original alphabet. Though it was a distinct creation, the core alphabetic idea was not independently discovered.
> If you count syllabic writing systems (which are not technically alphabetic, but are more so than Chinese, or Mayan or Egyptian hieroglyphics), there are more: Japanese hiragana and katakana, Cherokee syllabics, Pahawh Hmong, Vai (West Africa), and Linear B (and presumably Linear A).
Syllabic writing systems are significantly less powerful than the alphabet (hence why they have generally been superceded by alphabetic ones).
They have been invented multiple times, so you can argue the smooth slope goes up to syllabic writing, sure. But only once has that led to an alphabet.
> There's also Thaana
I hadn't heard of this, but Wikipedia seems to suggest it's descended from Phoenician like everything else (although it has made the step from abjad -> alphabet).