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We present the latest results of our search for planets with HARPS-N at the3.6 m Telescopio Nazionale Galileo under the Tracking Advanced PlanetarySystems project: an in-depth study of the 15 most Li abundant giants from thePennState - Toru\'n Planet Search sample. Our goals are first, to obtain radialvelocities of the most Li-rich giants we identified in our sample to search forpossible low-mass substellar companions, and second, to perform an extendedspectral analysis to define the evolutionary status of these stars. Methods.This work is based on high-resolution spectra obtained with the Hobby-EberlyTelescope and its High Resolution Spectro- graph, and with the HARPS-Nspectrograph at the Telescopio Nazionale Galileo. Two stars, HD 181368 and HD188214 , were also observed with UVES at the VLT to determine berylliumabundances. We report i) the discovery of two new planetary systems around theLi-rich giant stars: HD 238914 and TYC 3318-01333- 1 (a binary system); ii)reveal a binary Li-rich giant, HD 181368 ; iii) although our current phasecoverage is not complete, we suggest the presence of planetary mass companionsaround TYC 3663-01966-1 and TYC 3105-00152-1 ; iv) we confirm the previousresult for BD+48 740 and present updated orbital parameters, and v) we find alack of a relation between the Li enhancement and the Be abundance for thestars HD 181368 and HD 188214 , for which we acquired blue spectra. We foundseven stars with stellar or potential planetary companions among the 15 Li-richgiant stars. The binary star frequency of the Li-rich giants in our sampleappears to be normal, but the planet frequency is twice that of the generalsample, which suggests a possible connection between hosting a companion andenhanced Li abundance in giant stars. We also found most of the companionsorbits to be highly eccentric.

Tracking Advanced Planetary Systems (TAPAS) with HARPS-N. VI. HD 238914 and TYC 3318-01333-1 - two more Li-rich giants with planets