Context. Stars are born together from giant molecular clouds and, if we assume that the priors were chemically homogeneous and well-mixed, we expect them to share the same chemical composition. Most of the stellar aggregates are disrupted while orbiting the Galaxy and most of the dynamic information is lost, thus the only possibility of reconstructing the stellar formation history is to analyze the chemical abundances that we observe today. Aims: The chemical tagging technique aims to recover disrupted stellar clusters based merely on their chemical composition. We evaluate the viability of this technique to recover co-natal stars that are no longer gravitationally bound. Methods: Open clusters are co-natal aggregates that have managed to survive together. We compiled stellar spectra from 31 old and intermediate-age open clusters, homogeneously derived atmospheric parameters, and 17 abundance species, and applied machine learning algorithms to group the stars based on their chemical composition. This approach allows us to evaluate the viability and efficiency of the chemical tagging technique. Results: We found that stars at different evolutionary stages have distinct chemical patterns that may be due to NLTE effects, atomic diffusion, mixing, and biases. When separating stars into dwarfs and giants, we observed that a few open clusters show distinct chemical signatures while the majority show a high degree of overlap. This limits the recovery of co-natal aggregates by applying the chemical tagging technique. Nevertheless, there is room for improvement if more elements are included and models are improved. Based on observations obtained at the Telescope Bernard Lyot (USR5026) operated by the Observatoire Midi-Pyrénées, Université de Toulouse (Paul Sabatier), Centre National de la Recherche Scientifique of France, and on public data obtained from the ESO Science Archive Facility under requests number 81252 and 81618.