How do we extend 第二天 ("next day") to other days ("previous day", "same day", etc.)?
You have to first understand what &quot;第&quot; means. It's used to point out the position of something from a sequence.
One, two, three, four, five, six: 一, 二, 三, 四, 五
First, second, third, fourth, fifth, sixth: 第一, 第二, 第三, 第四, 第五
So 第二天 isn't completely equal to &quot;next day&quot;, but &quot;the second day&quot;.
当天: same day (this is correct)
For &quot;previous day&quot;, you're basically trying to refer to the &quot;-1&quot; day from today, so &quot;第&quot; cannot be used here...like there's no &quot;negative first&quot; in English.
Only phrase I can think of now is &quot;前一天&quot;.
前: before, 一天: one day
so 前一天 = one day before = previous day
Example:
Today is his first day at work, but he started learning some related knowledge the previous day.
今天是他第一天上班, 但是他前一天就開始學習一些相關的知識。
Do keep in mind that 前天 means &quot;the day before yesterday&quot;, so don't confuse it with 前一天
Edit:
To reply Wayne's comment.. 隔夜 is most often used as an adjective and pretty much equivalent to &quot;overnight&quot; in English.
You can also use &quot;前一天的菜&quot; to refer to 隔夜菜.

I usually like to prepare lunch the previous day, then bring to work
the next day. 我平常喜歡前一天把午餐準備好，然後隔天帶去公司吃。


My girlfriend wants to break up with my because I gave her my leftover
food from previous day(yesterday). She thinks overnight food is
disgusting. 我女朋友說要和我分手，因為我把我前一天(昨天)剩的飯給她吃。她覺得隔夜菜很噁心。

我平常喜歡隔夜把午餐做好 -&gt; (X)  This doesn't sound natural