When should I use "as part of", and when "as a part of"?
The difference between "as part of" and "as a part of" is essentially the difference between part and a part.
In the first case, part is used with the meaning an element or constituent that belongs to something and is essential to its nature. In the second case, part is used to mean a piece or segment of something such as an object, activity, or period of time, which combined with other pieces makes up the whole.
Other phrases uses part, and would have a different meaning (or no meaning) if they would use a part.
It depends on the speaker/writer. If the part can be separated from the whole, use "a part."
Actually, the person who mentioned countability was close to the mark.
It is a question of whether we can predict the size or number of parts.
If we can predict it, then we use a qualifier; otherwise, no quantifier.
Note that articles (a, an, the) are quantifiers; also words such as "some", "any", "no", etc.
There's probably a better term than "predictable", but I think you get the drift.
Can I have part of that pizza?
I hope to receive part of the profits.
Did you have any part in what happened?
I took no part in it.
We all have a part to play in fighting the battle against crime.
We all have some part to play in fighting the battle against crime.
I liked the part where he suddenly …
Part is used as both countable and uncountable, an example of the first case is
But there is a tendency to use part in the plural when it is treated as uncountable and that's why we seldom find "a part of" (but we can of course use "the part"). Example: