Consider an ODE system $$\dot x = f(t, x), \quad x(0) = \xi.$$ A collocation method to solve this ODE (1) assumes that $x$ can be approximated as a polynomial $x(t) \approx \sum_kx_kp_k(t)$ and (2) chooses the coefficients $\{x_k\}$ so that the initial condition is satisfied and so that the ODE is exact at some finite set of times $\{c_0, \ldots, c_m\}$. Usually we assume that $c_0$ is the left endpoint of the subinterval and that the coefficients are chosen so that the value of the solution at this left endpoint matches either the initial condition or the final value from the previous sub-interval. Collocation methods are equivalent to certain implicit Runge-Kutta methods and have various nice stability properties.
Nørsett and Wanner showed in Perturbed Collocation and Runge-Kutta methods that any Runge-Kutta method can be viewed as a kind of modified collocation method. The details of this modified collocation don't particularly matter for my question. What is important is that they assume in this paper that the collocation points $\{c_0, \ldots, c_m\}$ are all distinct.
It isn't strictly necessary to assume that all the collocation points are distinct in general. When a collocation point has multiplicity higher than 1, we require not just that the ODE is exact at that point, but that higher derivatives match as well. This is the basis for higher-derivative methods, which are described in section II.13 of Solving ODE I.
My question: If we allow for higher-derivative collocation methods, can we simplify the mapping of collocation methods onto all RK methods? For example, while collocation methods with distinct points $\{c_0, \ldots, c_m\}$ are always equivalent to implicit Runge-Kutta methods, we can recover boring old explicit Euler by taking $c_0 = c_1 = 0$. This is in fact the simplest Hermite-Obreschkoff method. I tried finding all references to the Nørsett and Wanner 1981 paper in google scholar and came up empty.
