Analyzing sequence count data, such as microbiome or gene expression data, poses a challenge. Researchers often want to estimate linear and non-linear effects of covariates on microbial or gene composition. Bayesian multinomial logistic-normal (MLN) models have gained popularity due to their ability to account for the count compositional nature of these data. However, inferring MLN models can be challenging. Recently, we developed a computationally efficient and accurate approach to inferring MLN models with a Marginally Latent Matrix-T Process (MLTP) form. Our approach is based on a particle filter with marginal Laplace approximation -- called the \textit{Collapse-Uncollapse} (CU) sampler. Here, we introduce a new class of MLN Additive Gaussian Process models (\textit{MultiAddGPs}) for additive deconvolution of overlapping linear and non-linear effects. MultiAddGPs can be efficiently inferred using the CU sampler. Furthermore, we develop an efficient approach to hyperparameter selection via Maximum Marginal Likelihood estimation. We validate our approach via both simulated and real data studies. The code is now available: https://cran.r-project.org/web/packages/fido/index.html