I have a military that needs to get around tanks Active Protection System. (APS). The idea is to have a anti-tank guided missile fire smaller missiles when the big missile gets close to a target. So that the smaller missiles use up the rounds of the active protection system. Allowing the main missile to hit the tank without being shot down by it's APS. Could this concept work?
Probably not, no
...because most ATGMs do not know how far away the tank is, it just keeps going in the direction that is indicated by the guidance system, and waits for its sensors to tell it that it has slammed into — or is near — a large metal body before going "Witness Me!!!"
By the time the missile triggers, it has already been defeated
Another problem is that the protection system is not triggering on proximity, but has been following this projectile for quite some while (in computer time, not slow squishy human brain time) before it arrives. So — while it might become a little confused — it has probably already decided when to activate, before the missile fires its decoy.
So, no, missiles lack the necessary information to use that concept.
Much more likely to succeed, is to make the missile strike from the top. The higher you can go, the more difficult it is for the active protection system to reach it. You can even stipulate that the system in your instance has a "blind" sector in which it cannot reach.
Not only is this strategy possible, it's already in use today (or at least a similar strategy). It's only a bit difficult to tell, because this technological capability is something that military forces obviously keep close to the vest.
For example, the US Military (specifically the Air Force and the Navy) have access to the MALD or Miniature Air-Launched Decoy. This is a decoy that's fired from an aircraft with the primary purpose of "suppressing air defenses" which roughly means forcing the enemy to expend AA resources and potentially reveal the locations of hidden AA locations prior to an assault or to deny them airspace out of threat of retaliation. Modern variants of this missile also have more advanced payloads like radar jammers or combat information interlink systems that allow them to network with nearby missiles, planes, or AWACS so that they can perform coordinated maneuvers and do things like escort a real cruise missile to it's destination and hopefully soaking up incoming AA.
Similarly, nuclear-tipped ICBMS almost always have a whole bunch of decoys that deploy from the tip of the missile to disguise which warheads are live and make it more difficult for interception systems to take them out. These are generally referred to as "penetration aids" and include all sorts of wacky technology to make it more difficult to shoot down. These include radar blocking chaff, maneuverable warheads, deployable Mylar balloons, and more.
If you're looking specifically for an AT weapon which splits apart after being fired, it probably only exists in a Defense Contractor's lab somewhere right now, but the reason they don't exist is because recent warfare has been extremely asymmetrical. What's really in-vogue right now are so-called "loitering munitions" which are essentially fire-and-forget kamikaze drones. One or more of these can be fired, and then using a combat information system, they can link up and, for example, all line up their flight paths so they impact a single target simultaneously from different directions. Fire control computers in modern military weapons also have similar functionality, and multiple artillery pieces or guns can be linked together so that they all hit the target at the same time even if they are at different distances/angles to saturate the opponent's defenses.
If you really want to feel like a morally-compromised arms dealer, watch this:
As far as the public is aware today, there is no ATGM which splits into several decoys after being launched to distract a tank's APS system. What does exist however are smart weapons systems which can work together to overwhelm an APS by making the attacks happens simultaneously or shortly after eachother. Most APS systems today are vulnerable to such a strategy, because they are explosive in nature and take time to reload or have a limited number of charges before they need to be replaced. Also, modern military weapons are really smart and it is totally plausible that such a weapon could exist today (or even 10 years ago).