The assessment of the frequency of planetary systems reproducing the solar system's architecture is still an open problem in exoplanetary science. Detailed study of multiplicity and architecture is generally hampered by limitations in quality, temporal extension and observing strategy, causing difficulties in detecting low-mass inner planets in the presence of outer giant planets. We present the results of high-cadence and high-precision HARPS observations on 20 solar-type stars known to host a single long-period giant planet in order to search for additional inner companions and estimate the occurence rate f_p_ of scaled solar system analogues - in other words, systems featuring lower-mass inner planets in the presence of long-period giant planets. We carried out combined fits of our HARPS data with literature radial velocities using differential evolution MCMC to refine the literature orbital solutions and search for additional inner planets. We then derived the survey detection limits to provide preliminary estimates of f_p_. We generally find better constrained orbital parameters for the known planets than those found in the literature; significant updates can be especially appreciated on half of the selected planetary systems. While no additional inner planet is detected, we find evidence for previously unreported long-period massive companions in systems HD 50499 and HD 73267. We finally estimate the frequency of inner low mass (10-30M_{earth}_) planets in the presence of outer giant planets as f_p_<9.84% for P<150-days. Our preliminary estimate of f_p_ is significantly lower than the literature values for similarly defined mass and period ranges; the lack of inner candidate planets found in our sample can also be seen as evidence corroborating the inwards-migration formation model for super-Earths and mini-Neptunes. Our results also underline the need for high-cadence and high-precision followup observations as the key to precisely determine the occurence of solar system analogues.