Meaning:
“加” means “to add,” and “戏” means “role performing.” Literally this term refers to the scenario where an actor doesn’t strictly follow the script but gives themselves the freedom to “improvise,” to add more aspects to their roles in a movie or TV series. Metaphorically, it is used to mock people who exaggerate, over-interpret and overreact to things to the extent that other people may dislike them. Sometimes, it’s used between close friends or on oneself jokingly.
Example:
A: 那天下班刚好下雨，同事就开车送我回家，我发现他一直朝我坐的副驾驶位看，以为他对我有好感。
Nàtiān xiàbān gānghǎo xiàyǔ，tóngshì jiù kāichē sòng wǒ huíjiā，wǒ fāxiàn tā yīzhí cháo wǒ zuò de fùjiàshǐwèi kàn，yǐwéi tā duì wǒ yǒu hǎogǎn。
It started to rain when I was to leave the office that day, and my colleague offered to give me a ride. I was sitting beside him in the front row. Then I noticed that he was constantly looking my way while he drove. I thought he had a crush on me.
B: 难道不是吗？
Nándào búshì ma？
Isn’t that the case?
A: 我纯粹是给自己加戏，人家是看后视镜。
Wǒ chúncuì shì gěi zìjǐ jiāxì，rénjiā shì kàn hòushìjìng。
I “improvised” and misinterpreted his intentions. He was just checking the right rear view mirror.