[reason],(再)加上 + [reason],所以 / 就 + [result]
再加上 adds a second reason to the first, and the two together lead to a result. It starts the second reason, and 所以, 就 or 才 usually introduces the result.
加上 alone means the same and is a little lighter. 再 stresses that this is one more thing.
The reason after 再加上 can be a clause or just a noun phrase.
再加上 piles up causes. For a plain "also" with no result in view, use 也, 还 or 而且.
加上 is also the plain verb "add": 加上我,一共五个人 is "five people, counting me".