Hungry ghost / Master of Many styles monk

[Darren Pfeffer]

I saw that this was a possible double archetype and was wondering the best way to go about doing this I've seen people do snake and panther style using the kick from hungry ghost to maximize attacks per round but am unsure if that's the best route/ how that interaction fully works

[Tyrant Lizard King]

I can't find any styles that would grant extra attacks from using Punishing Kick.

Master of Many Styles is very fun and there are plenty of style combos that work well together. There are a TON of newer styles I'm not familiar with. Here are a couple combos for consideration/inspiration.

Snake, Crane and Snapping Turtle make a good defensive style.
Dragon, Tiger and Boar make a powerful offensive style.
Monkey and Mantis mix well to cripple opponents.
Panther and Janni make a highly mobile offensive style.
Dragon, Marid, Shaitan, Efreeti and Djinni to have an elemental mastery style.