I wonder if maybe the following is on your mind:
Let's say we read a news report that says: "The growth of the swarm of locusts is accelerating." (When locusts swarm they shorten their reproductive cycle, thus accelerating the rate at which the swarm grows.)
Let's say the size of the swarm is represented in terms of the combined biomass of the swarm. Given a defined size of the swarm the rate-of-growth of the swarm is defined and then the time derivative of rate-of-growth is acceleration of the rate-of-growth.
Obviously, in order for rate-of-growth to exist, and for rate-of-rate-of-growth to exist, the size of the thing must be a definable state. (It would be absurd to suggest: there is no such thing as 'the size of the swarm', but we can meaningfully say that growth of the swarm is accelerating.)
So, does similar logic apply in theory of motion?
That is, we have that velocity is the time derivative of position, and that acceleration is the time derivative of velocity. If it is claimed that acceleration is absolute does that logically imply that whatever it is a derivative of must be absolute too?
My understanding is that in theory of motion this is dealt with as follows:
The set of all coordinate systems with a uniform velocity with respect to each other is defined as an equivalence class of inertial coordinate systems. Mathematically, acceleration with respect to that equivalence class is uniquely defined because with respect to every member of the equivalence class of inertial coordinate systems acceleration is the same.
So this is an example where a mathematical property (a property of the operation of taking a derivative) is applied as a physics theory.