Despite the several available strategies to build complex supramolecular constructs, only a handful of different molecular knots have been synthesised so far. Here, in response to the quest for further designable topologies, we use Monte Carlo sampling and molecular dynamics simulations, informed by general principles of supramolecular assembly, as a discovery tool for thermodynamically and kinetically accessible knot types made of helical templates. By combining this approach with the exhaustive enumeration of molecular braiding patterns applicable to more general template geometries, we find that only few selected shapes have the closed, symmetric and quasi-planar character typical of synthetic knots. The corresponding collection of admissible topologies is extremely restricted. It covers all known molecular knots but it especially includes a limited set of novel complex ones that have not yet been obtained experimentally, such as 10124 and 15n41185, making them privileged targets for future self-assembling experiments.