Signature-based writer identification (SWI) is an automated segmentation-free holistic approach where a person is identified based on their handwritten signature. Earlier research attempts mainly featured learning-based approaches where writing patterns were detected and fed to machine learning models for determining the writer. Nowadays, a deep learning-based approach is becoming very popular and several works are reported in the literature using such models. In this paper, we propose a two-stage convolution neural network (CNN) architecture that has two properties: (i) at first, two state-of-the-art CNN models namely VGG-19 and EfficientNet-B0 were truncated making them lightweight; (ii) Secondly, a stack ensemble network (SEN) was proposed where the truncated architectures were stacked along with a shallow base CNN model. The proposed system experimented on a newly built multi-script offline signature dataset where three popular Indic scripts namely: Bangla, Roman and Devanagari were considered. The proposed SEN outperforms individual CNN architectures in terms of recognition rate. In addition, the system converges considerably fast as the SEN architecture is shallower compared to heavier traditional networks. Overall, we obtained the highest writer identification accuracy of 99.44%, 99.04%, and 98.61% for Bangla, Roman, and Devanagari, respectively, by the proposed SEN architecture. Furthermore, the dataset used in this paper will be available freely for research purposes from the link mentioned in Section III.