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In the next decade, transient searches from the Vera C. Rubin Observatory and the Nancy Grace Roman Space Telescope will increase the sample of known Type Ia Supernovae (SN Ia) from $\sim10^3$ to $10^5$. With this reduction of statistical uncertainties on cosmological measurements, new methods are needed to reduce systematic uncertainties. Characterizing the underlying spectroscopic evolution of SN Ia remains a major systematic uncertainty in current cosmological analyses, motivating a new simulation tool for the next era of SN Ia cosmology: Build Your Own Spectral Energy Distribution (BYOSED). BYOSED is used within the SNANA framework to simulate light curves by applying spectral variations to model SEDs, enabling flexible testing of possible systematic shifts in SN Ia distance measurements. We test the framework by comparing a nominal Roman SN Ia survey simulation using a baseline SED model to simulations using SEDs perturbed with BYOSED, and investigate the impact of neglecting specific SED features in the analysis. These features include semi-empirical models of two possible, predicted relationships: between SN ejecta velocity and light curve observables, and a redshift-dependent relationship between SN Hubble residuals and host galaxy mass. We analyze each BYOSED simulation using the SALT2 & BBC framework, and estimate changes in the measured value of the dark energy equation-of-state parameter, $w$. We find a difference of $Δw=-0.023$ for SN velocity and $Δw=0.021$ for redshift-evolving host mass when compared to simulations without these features. By using BYOSED for SN Ia cosmology simulations, future analyses (e.g., Rubin and Roman SN Ia samples) will have greater flexibility to constrain or reduce such SN Ia modeling uncertainties.