$Gaia$ and its complementary spectroscopic surveys combined will yield the most comprehensive database of kinematic and chemical information of stars in the Milky Way. The $Gaia$ FGK benchmark stars play a central role in this matter as they are calibration pillars for the atmospheric parameters and chemical abundances for various surveys. The spectroscopic analyses of the benchmark stars are done by combining different methods, and the results will be affected by the systematic uncertainties inherent in each method. In this paper, we explore some of these systematic uncertainties. We determined line abundances of Ca, Cr, Mn and Co for four benchmark stars using six different methods. We changed the default input parameters of the different codes in a systematic way and found, in some cases, significant differences between the results. Since there is no consensus on the correct values for many of these default parameters, we urge the community to raise discussions towards standard input parameters that could alleviate the difference in abundances obtained by different methods. In this work, we provide quantitative estimates of uncertainties in elemental abundances due to the effect of differing technical assumptions in spectrum modelling.