Detailed band structures of three chiral-candidate nuclei, 134Pr, 132La and 103Rh have been studied. The aim of the study was twofold. First, to try to explore the reasons behind the contradiction between the theoretically predicted chirality in these nuclei and the recently observed fingerprints that suggest non-chiral interpretation for the previous chiral candidate band doublets. Second, to search for multiple chiral bands of different types in these nuclei. In 134Pr a new πh11/2vh11/2 band has been observed besides the previously known chiral-candidate πh11/2vh11/2 doublet. This new band and the yrare πh11/2vh11/2 band show the expected features of a chiral doublet structure. This fact combined with the observed similarity between the band structures of 134Pr and 132La suggests that chirality might exist in these nuclei. The detailed study of the 103Rh band structure resulted in the observation of two new chiral-doublet looking structures besides the previously known one. This is indicative of possible existence of multiple chiral doublet structure in this nucleus.