besides
in addition
furthermore
Structure
- その上 + Phrase
[often used in formal settings]
Is その上 relatively formal; while 上に is less so?
Hey! Both of these grammar points can be interpreted differently since 上に is a noun + a particle and その上 is a conjunction. However, in the majority of contexts both その上 and 上(に) are interchangeable and the level of formality is negligible. Cheers!
hmm… Sorry, I’m still not following. These sound so similar.
The English translations use the same words:
なお = in addition, incidentally, furthermore, moreover
その上 = besides, in addition, furthermore
The structures are the same:
Phrase1. なお 、+ Phrase2
その上 + Phrase
Every example in Bunpro uses two phrases, so even though その上 doesn’t say Phrase1, there’s always a Phrase1.
They’re both in the formal register.
How do I distinguish these two from each other?
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Hey @FredKore 
I tried to describe it a bit, I hope it will be understandable.
So when なお is used as an adverb meaning “even more” or “still” it can be replaced with そのうえ.
彼女は綺麗で、そのうえ、あたまもいい。
彼女は綺麗で、なお、あたまもいい。
She is pretty and on top of that smart.
On the other hand, when なお is used as a conjunction it cannot really be replaced with そのうえ because they are used in different situations.
そのうえ introduces some additional, similar statement with emphasis. For example, can be used to describe two situations, states, reasons. Notice that clause following そのうえ often contains “も” or “まで”.
昨日は夜遅くまで編み物をしてしまった。その上、朝早くから電話で起こされたのでとても眠いです。
I stayed up late last night knitting. Furthermore (on top of that) , I was woken up early by a phone call so I am really tired.
Two reasons are stated.
今日はとても寒かった。その上、雨まで降ってきたので屋外のアルバイトは大変だった。
It was very cold today. In addition (on top of that) , it decided to rain so my outdoor part-time job was really rough.
Again, two reasons were stated.
顔が青白い。その上、唇は紫だ。大丈夫だろうか？
His face is pale. Furthermore(on top of that) , his lips are purple. Is he okay, I wonder?
Two descriptions of someones state.
この携帯電話を無料で差し上げます。そのうえ1ヶ月はWi-Fi の料金も無料になります。
We will provide you this phone free of charge. On top of that, you will get one month of wi-fi for free.
On the other hand, when なお is used at the beginning of the sentence, it is usually at the end of some kind of notification, formal written request, legal note in the book, license, academic papers, and so on providing some kind of a condition (usually exception, for example, that credits cards are not accepted) or additional supplementary information (for example, if you get invitation to a meeting, main part will describe what kind of meeting it is and なお part will add details where exactly the meeting will take place, when and so on) to whatever has been in the main body of the notice. The most important part should appear before なお.
Example 1: you receive notification that you have been selected to receive a prize, and after the main body of the notification, there is this special condition mentioned that if you cannot come, please contact the people responsible in advance.
なお、万一ご欠席になる場合は、事前にご一報いただければ幸いです。
In addition (however) If you will not be able to attend the meeting, we would appreciate it if you could let us know in advance.
Another example, you get some notification about membership fee for adults, and exception for children follows なお.
会費は２０００円です。尚、小学生以下は無料です。
The fee is 2000 yen. In addition (however) it is free for elementary school students and younger.
Another example, you get a notification about a wedding and some supplementary info follows (adding details to the main part).
結婚式は7月15日に執り行います。尚、招待状は、他日正式に送らせていただきます。
そのうえ is not really used to provide conditions or details to the previous statements. なお is also not really used to provide additional reasons, similar statements or situations, but simply adding some details to main body.
そのうえ is closer to しかも, さらに。
なお is closer to また, ただし (exceptions).
I hope it helps,
Cheers
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Thank you for the detailed reply! 
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