These are all AP-1 motifs, that is a transcription factor family that all these members belong to (Fos, Jun, ATF...).
They all share a similar motif, that is why they belong to the same family. Having similar or almost identical motifs is very common for transcription factors. It is then the experssion level, affinity of each transcription factor for the actual DNA target sequence and interaction with binding partners that determines whether a TF binds or not. Competition between members of the same family for the same binding sites have extensively been reported in the literature. Ratios of expression levels can be important regulatory mechanisms towards gene expression.
Motifs are just rough approximations towards the actual factors. You will need to take expression data of these factors, ideally also protein expression and binding data such as ChIP-seq into account. Once you have candidates you would need to make experiments, such as knockout and overexpression to prove your in silico results. That having said, motifs alone are probably not sufficient to make convincing claims.