I’m afraid I must disagree with you. To me, “some pieces of advice” sounds either illiterate or jocular; the reason why you would not say it that way is that “some advice” already covers the same meaning.
We say “a piece of advice” only when we want to emphasize that some advice consists of only one discrete point or item, as opposed to a longer argumentation or something like that; using the word “piece” is rather a trick, because we lack a singular form for the uncountable noun “advice”; we use “piece” only when there is no other option. When some advice consists of more than one item, we can thankfully fall back to the collective noun: some advice. We do use the plural, however, when we are talking about a definite number: three pieces of advice.
I suppose the same applies to all uncountable nouns that can go with “a piece of”, or with some other “a … of” that expresses a part of it: some information, some bread, some cake.
Note that the difference between “some advice” and “a piece of advice” is sometimes vague; for what is a discrete item, and what is a longer argumentation? This distinction sometimes cannot be made; when in doubt, do not use “piece”.
“Some pieces of advice” could perhaps be defended if it were used to describe a list of unrelated items that were each a “piece of advice” but could not be taken as a consistent whole; but even then it would be doubtful, since “some advice” would still be possible; and you would rarely present such a list, let alone ask for one.
You could try searching Google for the following:
site:*.co.uk "some pieces of advice"