What would happen to the order of #A# if its concentration is increased to a very large amount for an initially first-order reaction?

If nothing else is in the reaction, then nothing would occur, because #A# must change concentration in a first-order reaction where it is by itself.

But...

...It also depends on what else is in the reaction. If the first-order reactant is #A# and another reactant is #B# of unknown order, and you have a lot of #B# but only a little #A#, #A# will change concentration by much more than #B# would.

In that case, even for the reaction

#A + B -> C#,

with #[B]# #">>"# #[A]#, the rate law would effectively be

#r(t) = k[A]^1[B]^n ~~ k[A]#, #" "n ~~ 0#

since #B# basically not changing concentration is effectively zero order with respect to #B#.

This is what you would call pseudo-first-order with respect to #A#.

In this case, suppose you had #"50 M"# of #A# and #"10 M"# of #B#. If you double #[A]#, you could say that since #A# is then 100 times the concentration of #B#, you approximate

#[A] ">>" [B]#.

Then #A# will become effectively zero order while the reaction will be based on the order of effectively only #B#.

So the order of #A# slightly decreases as you increase the concentration of #A#, until it reaches zero order at infinitely large concentration.