The assessment of the frequency of planetary systems reproducing the Solar Systems architecture is still an open problem. 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 planetary bodies. 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 analogs, i.e. systems featuring lower-mass inner planets in the presence of long-period giant planets. We carry 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 derive 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. 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 (10-30 M$_oplus$) 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 values found in the literature; the lack of inner candidate planets found in our sample can also be seen as evidence corroborating the inward migration formation model for super-Earths and mini-Neptunes. Our results also underline the need for high-cadence and high-precision follow-up observations as the key to precisely determine the occurence of Solar System analogs.
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