We report on the stability of hypothetical super-Earths in the habitable zone of known multiplanetary systems. Most of them have not yet been studied in detail concerning the existence of additional low-mass planets. The new N-body code GENGA developed at the University of Zürich allows us to perform numerous N-body simulations in parallel on graphics processing units. With this numerical tool, we can study the stability of orbits of hypothetical planets in the semimajor axis and eccentricity parameter space in high resolution. Massless test particle simulations give good predictions on the extension of the stable region and show that HIP 14810 and HD 37124 do not provide stable orbits in the habitable zone. Based on these simulations, we carry out simulations of 10 M⊕ planets in several systems (HD 11964, HD 47186, HD 147018, HD 163607, HD 168443, HD 187123, HD 190360, HD 217107 and HIP 57274). They provide more exact information about orbits at the location of mean motion resonances and at the edges of the stability zones. Beside the stability of orbits, we study the secular evolution of the planets to constrain probable locations of hypothetical planets. Assuming that planetary systems are in general closely packed, we find that apart from HD 168443, all of the systems can harbour 10 M⊕ planets in the habitable zone.