We focus attention on the combinations of swiftly growing electromagnetic instabilities (EMI) arising in the interaction of relativistic electron beams (REB) with precompressed deuterium-tritium (DT) fuels of fast ignition interest for inertial confinement fusion (ICF). REB-target system is taken neutral in charge and current with distribution functions including target and beam temperatures. We stress also the significant impact on modes growth rates (GR) of mode-mode coupling and intrabeam scattering. Collisional damping is documented at large wave numbers in terms of inverse skin depth. A quasi-linear approach yields lower GR than linear ones. One of the most conspicuous output of the linear analysis are three-dimensional (3D) broken ridges featuring the largest GR above k-space for an oblique propagation w.r.t initial particle beam direction. The given modes are seen immune to any temperature induced damping. Those novel patterns are easily produced by considering simultaneously Weibel, filamentation and two-stream instabilities. The behaviors persist in the presence of smooth density gradients or strong applied magnetic fields. Moreover, in the very early propagation stage with no current neutralization in the presence of large edge density gradients, REB demonstrate a characteristics ringlike and regularly spiked pattern in agreement with recent experimental results and previous simulations.