The rapid progression in Information and Communication technologies leads to an exponential increase in authenticity and copyright concerns of digital media. Watermarking of digital media is the solution to this issue. The traditional watermarking schemes use a single value or fixed value of embedding factor to embed a watermark into the host image, leading to inferior visual quality and robustness. To overcome this issue, this work proposes multiple scaling factors (MSF) based scheme using discrete shearlet transform (DST) and discrete cosine transform (DCT) for color images. The coati optimization algorithm (COA) is employed to adaptively optimize the values of MSF locally based on different regions in varying images. For embedding a watermark, the approximation coefficient matrix obtained using DST is divided into non-overlapping blocks. Subsequently, using the MSF, an encoded watermark is embedded into the DC coefficients obtained after applying DCT to each block. Furthermore, for enhanced security, the proposed scheme used Arnold’s chaotic map to encode the watermark. The experimental findings show that the proposed scheme achieves high visual quality with a median SSIM and PSNR value of 0.994 and 62.581 dB, respectively. In addition, the proposed scheme shows resilience to different image-processing attacks. Moreover, a comparison of the proposed scheme with the state-of-the-art scheme reveals its superiority in terms of visual quality and robustness.