We present the first simulations within an effective theory of structure formation (ETHOS), which includes the effect of interactions between dark matter and dark radiation on the linear initial power spectrum and dark matter self-interactions during non-linear structure formation. We simulate a Milky Way-like halo in four different dark matter models and the cold dark matter case. Our highest resolution simulation has a particle mass of $2.8times 10^4,{rm M}_odot$ and a softening length of $72.4,{rm pc}$. We demonstrate that all alternative models have only a negligible impact on large scale structure formation. On galactic scales, however, the models significantly affect the structure and abundance of subhaloes due to the combined effects of small scale primordial damping in the power spectrum and late time self-interactions. We derive an analytic mapping from the primordial damping scale in the power spectrum to the cutoff scale in the halo mass function and the kinetic decoupling temperature. We demonstrate that certain models within this extended effective framework that can alleviate the too-big-to-fail and missing satellite problems simultaneously, and possibly the core-cusp problem. The primordial power spectrum cutoff of our models naturally creates a diversity in the circular velocity profiles, which is larger than that found for cold dark matter simulations. We show that the parameter space of models can be constrained by contrasting model predictions to astrophysical observations. For example, some models may be challenged by the missing satellite problem if baryonic processes were to be included and even over-solve the too-big-to-fail problem; thus ruling them out.
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