No it's not possible. The thing that makes Sars-Cov-2 unique is its binding site in the human body. Sars-Cov-2 binds to the ACE2 receptor, which is found in just about every organ in your body. Unlike many other viruses which target receptors more localized to e.g. your throat/airway, Sars-Cov-2 can infect cells in your nasal cavity, stomach, lungs, heart, olfactory neurons, you name it. And every cell it infects will be destroyed; either by bursting to release the viral replicas, or by an immune system response.
Seasonal flu is multiple different strains that can exchange genetic material, as contrasted with COVID that doesn't have different strains but small mutations
I'm not sure that damage to various organs around the body beyond respiratory system is that a unique of a property - see myocarditis and the like related to influenza infection, which is a significant cause of mortality.
