Responsibility uncountable?

It just occurred to me that many English nouns can be countable and uncountable at the same time. For example, responsibility. You can say

That’s too much responsibility.
I have many responsibilities.

Am I correct or am I confusing something?
Also, is there a rule or a list of those nouns that can be both countable and uncountable?

Thanks to you all.

You are right that there are many, but no rule on which nouns can have those dual qualities. Intuitively, it seems to me that it would be more difficult for concrete nouns than for abstract nouns.

Hello Mister Micawber, what about the nouns food and accommodation. I have been told that they can be used in the singular form only (in British English) but a Google search shows that the plural forms (foods and accommodations) exist too. Is that American English?
Thank you.

I have no experience with BrE and am continually being caught out by the things they evidently say. What I can tell you is

(1) Foods is used mainly in two ways: when speaking of nutrition or other topics in which types of food are of the essence; and as a part of the names of food supply companies like Kraft Foods. Googling the word should give you sufficient examples.

(2) The dictionaries I have consulted indicate that accommodation and accommodations are used interchangeably to indicate hotel rooms, etc. Webster’s Collegiate says that it is ‘usually’ used in the plural form.