Consider a class of probability distributions which is dense in the space of all probability distributions on $\mathbb{R}^{d}$ with respect to weak convergence, for every $d\in\mathbb{N}$. Then, we construct various explicit classes of continuous (cádlág) processes which are dense in the space of all continuous (cádlág) processes with respect to convergence in distribution. This is motivated by the recent result that quasi-infinitely divisible (QID) distributions are dense when $d=1$. If this result is extended to any $d\in\mathbb{N}$, then our result will imply that QID processes are dense in both spaces of continuous and cádlág processes.