I would doubt it—different vaccines provoke different immune responses, and each has a dosing schedule based on empirical evidence about what produces the best response. The fact that two doses are needed for an optimal response from the covid vaccine doesn't tell you much about any other vaccine.
It's possible that two vaccines would produce a slightly better response but they decided the cost/benefit didn't pencil out, and I could imagine that for some immune compromised people, getting two would be appropriate. But I'd stick to the recommended schedule absent strong reasons for doing otherwise.
Caveat: I have a strong layperson's understanding of vaccines, but I haven't looked at data specifically for the flu vaccine.