The Seleucids went into a tailspin after the battle of Magnesia, and lost all their influence outside Syria. The huge reparations forced on them ruined their treasury and it was the reason why the Parthians and later, Jews, began to score victories against them routinely. The only reason they survived until Pompey era was because both Rome and Parthia found them a useful buffer state that was weak and did not impinge on their own interests. The key problem you need to solve is that the Seleucid army is in dire need of reform. Without the hardcore Macedonian infantry, and with them distrusting natives and relying only on Greek settlers for the core of their heavy infantry, the Seleucid army is poorly matched against the Romans, and simply does not have either the quality or quantity of the heavy infantry of the Romans. Against the other kingdoms with similarly weak infantry (like the Ptolemies and the Pontic Kingdom, who both had their imitation Macedonian pikemen), and the politically weak successor state of Macedonia, this army was adequate. But not against the Romans, with their superb legions. But Antiochus is too late to change that, apart from the personal mental make up of Antiochus makes it less likely that he will make any concessions to the non-Greek population of his kingdom.
What you really need to change is the structure of the Seleucid army. But by the time of Antiochus, the Romans and the Seleucids impinged on so many of each other's interests that a clash is coming before the Seleucid army has been reformed. The natural affinity of both the Romans and the Seleucids would be to clash over Greece (both claimed influence over that territory), and this clash is going to happen sooner or later. This is precisely what happened IOTL - Antiochus and the Romans clashed over a Green question, and the Seleucids were ruined. What you really need to do to have a Seleucid state of some consequence survive is for the Seleucids to either conquer Macedonia and establish themselves strongly in that territory, giving them a first rate infantry to rely on (too late for Antiochus to accomplish) or else, give the Seleucids time to draft and train native heavy infantry (which requires changing the structure of the Seleucid state, and consequently, takes time, even if Antiochus were willing to do so).
So - no. Antiochus III is too late to change anything much of consequence.