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Large-scale multi-modal contrastive pre-training has demonstrated great utility to learn transferable features for a range of downstream tasks by mapping multiple modalities into a shared embedding space. Typically, this has employed separate encoders for each modality. However, recent work suggests that transformers can support learning across multiple modalities and allow knowledge sharing. Inspired by this, we investigate a variety of Modality-Shared Contrastive Language-Image Pre-training (MS-CLIP) frameworks. More specifically, we question how many parameters of a transformer model can be shared across modalities during contrastive pre-training, and rigorously examine architectural design choices that position the proportion of parameters shared along a spectrum. In studied conditions, we observe that a mostly unified encoder for vision and language signals outperforms all other variations that separate more parameters. Additionally, we find that light-weight modality-specific parallel modules further improve performance. Experimental results show that the proposed MS-CLIP approach outperforms vanilla CLIP by up to 13\% relative in zero-shot ImageNet classification (pre-trained on YFCC-100M), while simultaneously supporting a reduction of parameters. In addition, our approach outperforms vanilla CLIP by 1.6 points in linear probing on a collection of 24 downstream vision tasks. Furthermore, we discover that sharing parameters leads to semantic concepts from different modalities being encoded more closely in the embedding space, facilitating the transferring of common semantic structure (e.g., attention patterns) from language to vision. Code is available at \href{https://github.com/Hxyou/MSCLIP}{URL}.