Text-to-image (TTI) diffusion models have demonstrated impressive results in generating high-resolution images of complex and imaginative scenes. Recent approaches have further extended these methods with personalization techniques that allow them to integrate user-illustrated concepts (e.g., the user him/herself) using a few sample image illustrations. However, the ability to generate images with multiple interacting concepts, such as human subjects, as well as concepts that may be entangled in one, or across multiple, image illustrations remains illusive. In this work, we propose a concept-driven TTI personalization framework that addresses these core challenges. We build on existing works that learn custom tokens for user-illustrated concepts, allowing those to interact with existing text tokens in the TTI model. However, importantly, to disentangle and better learn the concepts in question, we jointly learn (latent) segmentation masks that disentangle these concepts in user-provided image illustrations. We do so by introducing an Expectation Maximization (EM)-like optimization procedure where we alternate between learning the custom tokens and estimating masks encompassing corresponding concepts in user-supplied images. We obtain these masks based on cross-attention, from within the U-Net parameterized latent diffusion model and subsequent Dense CRF optimization. We illustrate that such joint alternating refinement leads to the learning of better tokens for concepts and, as a bi-product, latent masks. We illustrate the benefits of the proposed approach qualitatively and quantitatively (through user studies) with a number of examples and use cases that can combine up to three entangled concepts.