Personality assessment aims to infer stable personality traits from dynamic behaviors across language, voice, and facial cues. Since different personality dimensions are revealed through distinct behavioral perspectives, modeling trait-specific evidence is challenging. However, most existing approaches adopt a uniform multimodal fusion strategy across all dimensions, assuming identical modality contributions. This overlooks trait-specific modality preferences and introduces cross-modal interference. To address this issue, we propose a novel personality assessment framework called Traits Run Deeper, which consists of three components. Specifically, the Multimodal Foundation Representation (MFR) module constructs personality-oriented multimodal inputs and leverages psychology-informed semantic templates as anchors, enabling foundation models to capture trait-relevant information. Building upon MFR, the Trait-Specific Modality Fusion (TSMF) module acts as an asymmetric fusion mechanism, allowing each dimension to selectively exploit different modality pathways from modality-specific modeling to complementary fusion. Thus, TSMF captures heterogeneous modality preferences while reducing cross-modal contamination. Furthermore, the Distribution-Calibrated Personality Regression (DCPR) module mitigates label imbalance and central tendency bias through target distribution calibration, improving robustness and stability. Experimental results on the AVI Challenge 2026 validation set demonstrate the effectiveness of the proposed framework, reducing mean squared error (MSE) by approximately 25% compared with the baseline. Consistent improvements are observed on the official test set, where our method achieves the best performance and ranks first in the Personality Assessment Track. The source code will be made available at https://github.com/MSA-LMC/AVI2026.