This paper presents a new high-sensitivity PET geometry for high fidelity MRI-compatible PET breast imaging which can scan both breasts simultaneously and have: high sensitivity and resolution; compatibility with MR-breast imaged volume; complete visualization of both breasts, mediastinum and axilla; and a modular design. Whereas contemporary dedicated X-ray and molecular breast imaging devices only scan one breast at a time, this approach relies on an unconventional PET geometry, and is able to provide a PET field of view (FOV) larger than that from dedicated breast MRI. The system geometry is evaluated with GATE Monte Carlo simulations of intrinsic system parameters. Various sized lesions (4-6mm) having [6:1 to 4:1] lesion:background radioactivity ratios mimicking different biological uptake are simulated, strategically located throughout a volumetric anthropomorphic torso. Dedicated breast PET (dbPET) imaging is compared with contemporary clinical PET. The dbPET system sensitivity is >6X greater than for contemporary whole-body PET. The novel, non-conventional system geometry allows for simultaneous dual-breast imaging, along with full medial and axillary imaging. Iteratively reconstructed full-volumetric images illustrate sharper visualization of 4mm lower uptake [4:1] lesions throughout the FOV compared with clinical PET. Image overlap between dedicated breast PET and MRI FOVs is excellent. Simulation results indicate clear superiority over conventional, high-sensitivity whole-body PET systems, as well as improved sensitivity over single-breast dbPET systems. This proposed system potentially facilitates both early detection and diagnosis, especially by increasing specificity of MRI, as well as visualizing tissue heterogeneity, monitoring therapeutic efficacy, and detecting breast cancer recurrence throughout the entire mediastinum.