While multimodal fusion has been extensively studied in Multimodal Sentiment Analysis (MSA), the role of fusion depth and multimodal capacity allocation remains underexplored. In this work, we position fusion depth, scalability, and dedicated multimodal capacity as primary factors for effective fusion. We introduce DeepMLF, a novel multimodal language model (LM) with learnable tokens tailored toward deep fusion. DeepMLF leverages an audiovisual encoder and a pretrained decoder LM augmented with multimodal information across its layers. We append learnable tokens to the LM that: 1) capture modality interactions in a controlled fashion and 2) preserve independent information flow for each modality. These fusion tokens gather linguistic information via causal self-attention in LM Blocks and integrate with audiovisual information through cross-attention MM Blocks. Serving as dedicated multimodal capacity, this design enables progressive fusion across multiple layers, providing depth in the fusion process. Our training recipe combines modality-specific losses and language modelling loss, with the decoder LM tasked to predict ground truth polarity. Across three MSA benchmarks with varying dataset characteristics, DeepMLF achieves state-of-the-art performance. Our results confirm that deeper fusion leads to better performance, with optimal fusion depths (5-7) exceeding those of existing approaches. Additionally, our analysis on the number of fusion tokens reveals that small token sets ($\sim$20) achieve optimal performance. We examine the importance of representation learning order (fusion curriculum) through audiovisual encoder initialization experiments. Our ablation studies demonstrate the superiority of the proposed fusion design and gating while providing a holistic examination of DeepMLF's scalability to LLMs, and the impact of each training objective and embedding regularization.