Yes, you're asking too much from a smaller negative. I've used many films anf several formats over the last 15 years, and have printed more than 20,000 photos in that time. About this time last year one of my friends was just getting interested in photography. I took him to Yosemite Valley one weekend and we spent two days shooting side-by-side. I had a Mamiya C330 system and he was using a Minolta manual focus with Minolta prime lenses. We both shot T-Max 100 and I developed all our negatives using Photographer's Formulary's T-Max developer. Even at 8x10 the differences in the formats are apparent. I printed them on my Beseler 4x5 enlarger using a Zone VI cold light head and EL-Nikkor lenses.(posted 9339 days ago)You say you can't afford even a second-hand medium format system, but you might be surprised. I have three Yashica Mat TLR camers and a Minolta Autocord. Total investment in all four is $800 US including repairs to two of the Yashica Mats. If you look around you can find an excellent TLR for under $300 US.
Having said that, you can get excellent 11x14 enlargements from 35mm T-Max 100 if you use a tripod while shooting. The prints won't show the smooth tonal gradations of a medium format negative, but you'll be pleased with the results until you get a medium format camera and start comparing the results.
BTW, my friend, after seeing the difference between our prints, bought a Crown Graphic for $200 and an old Schneider lens for $135. He's now hooked on 4x5 film.