The attribute of rotational profile to the hyperon puzzle in the prediction of heaviest compact star M. Bhuyan et al Since the discovery of neutron stars with masses around M 2 ⊙ the composition of matter in the central part of these massive stars has been intensively discussed. Within this paper we will (re)investigate the question of the appearance of hyperons. To that end we will perform an extensive parameter study within relativistic mean field models. We will show that it is possible to obtain high mass neutron stars with (i) a substantial amount of hyperons, (ii) radii of 12-13 km for the canonical mass of M 1.4 ⊙ , and (iii) a spinodal instability at the onset of hyperons. The results depend strongly on the interaction in the hyperon-hyperon channels, on which only very little information is available from terrestrial experiments up to now.