During its four years of photometric observations, the Kepler space telescope detected thousands of exoplanets and exoplanet candidates. One of Kepler's greatest heritages has been the confirmation and characterization of hundreds of multi-planet systems via transit timing variations (TTVs). However, there are many interesting candidate systems displaying TTVs on such long timescales that the existing Kepler observations are of insufficient length to confirm and characterize them by means of this technique. To continue with Kepler's unique work, we have organized the "Kepler Object of Interest Network" (KOINet), a multi-site network formed of several telescopes located throughout America, Europe, and Asia. The goals of KOINet are to complete the TTV curves of systems where Kepler did not cover the interaction timescales well, to dynamically prove that some candidates are true planets (or not), to dynamically measure the masses and bulk densities of some planets, to find evidence for non-transiting planets in some of the systems, to extend Kepler's baseline adding new data with the main purpose of improving current models of TTVs, and to build a platform that can observe almost anywhere on the northern hemisphere, at almost any time. KOINet has been operational since March 2014. Here we show some promising first results obtained from analyzing seven primary transits of KOI-0410.01, KOI-0525.01, KOI-0760.01, and KOI-0902.01, in addition to the Kepler data acquired during the first and second observing seasons of KOINet. While carefully choosing the targets we set demanding constraints on timing precision (at least 1 min) and photometric precision (as good as one part per thousand) that were achieved by means of our observing strategies and data analysis techniques. For KOI-0410.01, new transit data revealed a turnover of its TTVs. We carried out an in-depth study of the system, which is identified in the NASA Data Validation Report as a false positive. Among others, we investigated a gravitationally bound hierarchical triple star system and a planet-star system. While the simultaneous transit fitting of ground- andspace-based data allowed for a planet solution, we could not fully reject the three-star scenario. New data, already scheduled in the upcoming 2018 observing season, will set tighter constraints on the nature of the system. Ground-based photometry is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/615/A79