相まって・に加えて: the difference
相まってN1
Meaning
Combined with, Coupled with, Together with
Past papers
Tested once in past papers
Example
感動的なシーンとＢＧＭが相まって、泣かずにはいられませんでした。
The moving scene coupled with the background music made it impossible not to cry.
に加えてN2
Meaning
Not only...but also, In addition, Not to mention
Past papers
Example
今学期から文法に加えて漢字も教えることになった。
Starting this semester, in addition to grammar, I will also be teaching Kanji.
How to tell them apart
「相まって」: the point is that the two factors boost each other (1+1 is more than 2); there must be two elements.
「に加えて」: only simple addition, 'in addition to A there is B', without the idea of strengthening each other.