Aims. We present first results of our efforts to re-analyze the Kepler photometric dataset, searching for planetary transits using an alternative processing pipeline to the one used by the Kepler mission Methods. The SARS pipeline was tried and tested extensively by processing all available CoRoT mission data. For this first paper of the series we used this pipeline to search for (additional) planetary transits only in a small subset of stars -the Kepler objects of interest (KOIs), which are already known to include at least one promising planet candidate. Results. Although less than 1% of the Kepler dataset are KOIs we are able to significantly update the overall statistics of planetary multiplicity: we find 84 new transit signals on 64 systems on these light curves (LCs) only, nearly doubling the number of transit signals in these systems. Forty-one of the systems were singly-transiting systems that are now multiply-transiting. This significantly reduces the chances of false positive in them. Notable among the new discoveries are KOI 435 as a new six-candidate system (of which kind only Kepler-11 was known before), KOI 277 (which includes two candidates in a 6:7 period commensurability that has anti-correlated transit timing variations) -all but validating the system, KOIs 719, 1574, and 1871 that have small planet candidates (1.15, 2.05 and 1.71 R ⊕ ) in the habitable zone of their host star, and KOI 1843 that exhibits the shortest period (4.25 h) and is among the smallest (0.63 R ⊕ ) of all planet candidates. We are also able to reject 11 KOIs as eclipsing binaries based on photometry alone, update the ephemeris for five KOIs and otherwise discuss a number of other objects, which brings the total of new signals and revised KOIs in this study to more than one hundred. Interestingly, a large fraction, about ∼1/3, of the newly detected candidates participate in period commensurabilities. Finally, we discuss the possible overestimation of parameter errors in the current list of KOIs and point out apparent problems in at least two of the parameters. Conclusions. Our results strengthen previous analyses of the multi-transiting ensemble, and again highlight the great importance of this dataset. Nevertheless, we conclude that despite the phenomenal success of the Kepler mission, parallel analysis of the data by multiple teams is required to make full use of the data.