Is every language over any alphabets is accepted by automata?
Suppose that $\mathcal{M}$ is any kind of machine model in which every machine has a finite description, say as a binary string. The model can be more powerful than mere Turing machines – for example, it could be Turing machines with access to an oracle for the halting problem.

Since every machine has a finite description as a binary string, there are only countably many machines, and so countably many languages they accept. Since there are uncountably many languages, there must be some language not accepted by any $\mathcal{M}$-machine. In fact, most languages aren't, in the sense that a random language would not be accepted by any $\mathcal{M}$-machine.

The only way out is if machines do not have a finite description. But this is not what we usually understand by machine. An example of such a "machine" is one in which an arbitrary language is hardwired. Such machines can, by definition, accept all languages, but they are not so interesting mathematically.