Avoiding loose powders and resins, material extrusion additive manufacturing is a powerful technique to produce near-net shape parts, being a cheap and safe alternative for developing complex industrial-grade products. Filaments embedded with a high packing density of metallic or ceramic granules are being increasingly used, resulting in almost fully dense parts, whereby geometries are shaped, debinded and sintered sequentially until the completion of the part. Traditionally, “brown” debinded geometries are transported to conventional furnaces to densify the powder compacts, requiring careful tailoring of the heating profiles and sintering environment. This approach is decoupled and often involves time-consuming post-processing, whereby after the completion of the shaping and debinding steps, the parts need to be transported to a sintering furnace. Here, it is shown that sintering via indirect induction heating of a highly filled commercially available filament embedded with stainless steel 316L powder can be an effective route to densify Fused Filament Fabricated (FFF) parts. The results show that densities of 99.8% can be reached with very short soaking times, representing a significant improvement compared to prior methods. A hybrid machine is proposed, whereby a custom-built machine is integrated with an induction heater to combine FFF with local indirect induction sintering. Sintering in situ, without the need for part transportation, simplifies the processing of metal parts produced through material extrusion additive manufacturing.