Although additive manufacturing using multi-photon direct laser writing is nowadays considered as a major tool in the fabrication of future nano/micro-objects and optical components, it is currently limited by the low throughput of the writing process. To circumvent this issue, massive parallelization of the write process is a very promising avenue. However, simultaneous writing of structures in close spatial proximity generates fabrication artefacts, collectively referred to as "proximity effects", which strongly limit the accessible structure resolution. In this work, we systematically investigate the experimental parameters that influence these effects using specifically designed N×N spot diffractive optical elements. Through computer simulations, we show that these effects can be modeled remarkably successfully simply by taking Point Spread Function overlap and diffusion processes into account. We illustrate the usefulness of the concept by designing a parallel write approach giving access to periodic structures with short inter-object distances while very largely overcoming proximity effects.