If you want to see more films by Bong Joon-ho:Try Snowpiercer (2013). While any of Bong Joon-ho's films could prove interesting, I recommend Snowpiercer because, like Parasite, it deals with themes of class, want, and plenty, only in the context of an apocalyptic society. After a climate change apocalypse, the environment is too cold to support human life. The only people alive exist on Snowpiercer, a train that will never stop. A hierarchy of class exists on the train with first class passengers enjoying meat, comfy seats, and luxuries, the economy class traveling inside drawers that look suspiciously like mortuary cells, and the poorest class living in the crowded caboose, eating only Jello-like protein bars that bring to mind Soylent Green. A group of rebels, lead by Curtis (Chris Evans) plan to break out one of the economy passengers, a security specialist, in hopes that he and his daughter can bring them from the back to the engine, where they plan to demand equal treatment. The limited setting sets up a clever device of storytelling, where each train car forward means a new challenge, new dangers, and new secrets revealed. And like in Parasite, the further we travel with our heroes, the more unclear it becomes who is good, bad, trustworthy, or worth saving. Snowpiercer is available on Netflix.
If you found yourself rooting most for the ambitious young Ki-woo (sometimes called Kevin):Try Money (2019), directed by Park Noo-Ri. Il-hyun, a stockbroker-in-training, isn't doing so well and almost gets fired. Things seem to take a turn for the better when he meets "Ticket," an expert in insider trading that helps Il-hyun execute a $50 million trade. Now he's at the top, able to buy nice things, and even attract a girl. But working with Ticket means risks, too, and Il-hyun begins to wonder if his new success is worth the price. Like Parasite, this Korean movie starts with a young person using their wits to exploit an opportunity, but things take a darker turn.
If you like the funnier first half best:Try The Ladykillers (1955), directed by Alexander Mackendrick. Part of the fun of Parasite's first half is that the Kim family infiltrates the Park family house, living off their fat, while the Park family is none the wiser. In this British black comedy, sweet elderly Mrs. Wilberforce lives alone in a whimsical house in London. A stranger, Professor Marcus, approaches her, asking if she will allow him to rent space in her house, claiming he is part of a string quintet who needs rehearsal space. In actuality, they are a group if thieves planning a security van robbery. When Mrs. W meddles into their plans, they decide it's best to kill her, but things don't go according to plan. Although there was a remake, this version is definitely superior than the 2004 version. It's #13 on the BFI top 100 movies and has a rare 100% rating on Rotten Tomatoes.
If you want a straight-up Korean horror movie:Try Train to Busan (2016), directed by Yeon Sang-ho. Parasite turns shocking, bloody, and visceral towards the end. Train to Busan will get your pulse pounding as Seok-woo accompanies his young daughter back home on the titular train so she can see her mother for her birthday. An infected teenage girl slips onto the train unnoticed and starts a chain of zombie terror. The father-daughter pair team up with other passengers, all with their own stories, to survive. Train to Busan is a great example of Korean horror; although things become gory and stressful, there is an air of sentimentality throughout. We get to know our brave cast of survivors, and attention is given to family relationships, much more than is found in American horror. Bonus: Choi Woo-shik (Ki-woo) also is part of the cast, playing a baseball player traveling with his team. Train to Busan is available on Netflix.
For another deep dive into poverty and how it impacts and bonds a group living together as a family:Try Shoplifters (2018), directed by Hirokazu Koreeda. Although Parasite has moments of fun, surprise, and suspense, there's also more serious themes lurking underneath. Viewers may find themselves considering class, privilege, wealth, and morality, and there are layers upon layers of possible meaning. Shoplifters has a more serious tone and a heartwrenching tone throughout. A group living together shoplifts to make ends meet. They take in Yuri, who shows signs of being abused, but when a missing child report is aired on the news, the family has to hide to keep Yuri safe. Both movies show families living in poverty, doing what they believe is necessary to survive.
You can also read my review of Parasite.