Question

How could you keep an object's acceleration the same if the force acting on the object were doubled?

Answer 1

If the force on an object suddenly doubles, but for some reason you want
the object to keep the same acceleration, then you have only two choices:

#1). Immediately apply another new force to the object, in the direction opposite
to the first force, and equal to what the first force was before it doubled.

#2).  Somehow ... while it's accelerating ... glue more pieces onto the object
sufficient to double its mass.

Answer 2

$Force=mass*acceleration$
If you double the force, but want to keep acceleration the same, then you must double the mass as well.
$Force=mass*acceleration \\ (2)Force=(2)mass*acceleration$