The protein lysate array is an emerging technology for quantifying the protein concentration ratios in multiple biological samples. Statistical inference for a parametric quantification procedure has been inadequately addressed in the literature, mainly because the appropriate asymptotic theory involves a problem with the number of parameters increasing with the number of observations. In this article, we develop a multistep procedure for the Sigmoidal models, ensuring consistent estimation of the concentration levels with full asymptotic efficiency. The results obtained in the article justify inferential procedures based on large sample approximations. Simulation studies and real data analysis are used in the article to illustrate the performance of the proposed method in finite samples. The multistep procedure is convenient to work with asymptotically, and is recommended for its statistical efficiency in protein concentration estimation and improved numerical stability by focusing on optimization of lower-dimensional objective functions.