The relationship between electric potential and electric potential energy is like the relationship between electric field and electric force; in the sense that every electric charge produce an electric field (that has a particular value in any point in space), and it does that regardless of whether thare are any other charges around. But in order to talk about (electric) force, you need at least another charge in the picture, because what happens is that the electric field created by charge $q_1$ acts on the charge $q_{2}$ and accelerates it.
$$E\rightarrow V$$
$$F\rightarrow U$$$$E\ \overbrace{\rightarrow}^{\text{is for}} \ V$$ what $$F\ \overbrace{\rightarrow}^{\text{is for}} \ U$$
It's the same with electric potential and electric potential energy. A charge (or system of charges) produce an electric potential at any point in space, but we can only talk about electric potential energy between two charges (or between a system of charges and a test charge, for example).
So $E$ and $V$ refer to what a charge (or a system of charges) create in a particular point in space, while $F$ and $U$ are quantities (or terms) that refer to an interaction between two or more electrically charged entities.
The answer to your question "therefore is electric potential also defined for a system of charges?" is yes. The electric potential that a system of charges creates in a given point $P$ is:
$$V(P)=\frac{1}{4\pi\varepsilon_{0}}\sum_{j=1}^{N}\frac{q_{j}}{r_{jP}}$$ $N$ is the number of charges, $r_{jP}$ is the distance between charge $q_{j}$ and point $P$.