Periocular and face are complementary biometrics for identity management, albeit with inherent limitations, notably in scenarios involving occlusion due to sunglasses or masks. In response to these challenges, we introduce Flexible Biometric Recognition (FBR), a novel framework designed to advance conventional face, periocular, and multimodal face-periocular biometrics across both intra- and cross-modality recognition tasks. FBR strategically utilizes the Multimodal Fusion Attention (MFA) and Multimodal Prompt Tuning (MPT) mechanisms within the Vision Transformer architecture. MFA facilitates the fusion of modalities, ensuring cohesive alignment between facial and periocular embeddings while incorporating soft-biometrics to enhance the model's ability to discriminate between individuals. The fusion of three modalities is pivotal in exploring interrelationships between different modalities. Additionally, MPT serves as a unifying bridge, intertwining inputs and promoting cross-modality interactions while preserving their distinctive characteristics. The collaborative synergy of MFA and MPT enhances the shared features of the face and periocular, with a specific emphasis on the ocular region, yielding exceptional performance in both intra- and cross-modality recognition tasks. Rigorous experimentation across four benchmark datasets validates the noteworthy performance of the FBR model. The source code is available at https://github.com/MIS-DevWorks/FBR.