About a filter's rise time
When a system is linear, effects are proportional to causes. You can multiply the input by any constant, you'll get the same output multiplied by the same constant.

If you look at how the rise time is defined, you'll see that it is independent of any amplification factor.

You can also add two inputs, and the output will be the sum of the separate outputs corresponding to the separate inputs.

So it you apply a second, delayed step, there can be two situations


steady state (constant output) has been reached after the first step: then you can consider two distinct rises with equal times;
steady state has not been reached yet: there is a single, combined rise, with a different rise time.