Signature-based writer identification is an advanced automated technique that aims to recognize individuals based on their unique handwritten signatures. This method utilizes a holistic, segmentation-free approach, meaning that it examines the entire signature without breaking it down into smaller parts. However, many scripts used for training deep learning-based scene text detectors are low-resourced, making it challenging to build robust models. In real-world scenarios, it often occurs that a signature stored in a particular script needs to be verified against a current signature written in a different script. This discrepancy highlights the necessity for cross-script identification, which remains a relatively unexplored area. Historically, research in writer identification has predominantly relied on learning-based methods. These methods involved analyzing the distinctive writing patterns of individuals and feeding these patterns into machine learning models to identify the writer. Although effective to some extent, these traditional methods have limitations in handling the complexities of different scripts. Recently, deep learning techniques have gained significant traction due to their ability to learn and generalize from large amounts of data. Many contemporary studies now employ deep learning models to enhance writer identification accuracy. This paper introduces an innovative Convolutional Neural Network (CNN)-based framework specifically designed to tackle the challenges of cross-script identification. The framework is trained on one script with the part of another script and tested on second script, demonstrating its flexibility and robustness. The proposed system was rigorously tested using a newly created multi-script offline signature dataset. This dataset includes two widely used scripts: Bangla and Roman, providing a diverse testing ground for cross-script identification. The performance of our CNN-based framework was compared against standard CNN models, and the results were compelling. Our approach showed significant improvements in accuracy and reliability, suggesting that the technique is highly effective for cross-script signature identification.