The rapid proliferation of multimedia content has necessitated the development of effective multimodal video retrieval systems. Multimodal video retrieval is a non-trivial task involving retrieval of relevant information across different modalities, such as text, audio, and visual. This work aims to improve multimodal retrieval by guiding the creation of a shared embedding space with task-specific contrastive loss functions. An important aspect of our work is to propose a model that learns retrieval cues for the textual query from multiple modalities both separately and jointly within a hierarchical architecture that can be flexibly extended and fine-tuned for any number of modalities. To this end, the loss functions and the architectural design of the model are developed with a strong focus on increasing the mutual information between the textual and cross-modal representations. The proposed approach is quantitatively evaluated on the MSR-VTT and YouCook2 text-to-video retrieval benchmark datasets. The results showcase that the approach not only holds its own against state-of-the-art methods, but also outperforms them in a number of scenarios, with a notable relative improvements from baseline in R@1, R@5 and R@10 metrics.