It's possible. A1 scores and says, "Can't stop that!". B2: "F*** you!" Here is another example of offsetting technical fouls, without a fight.
However, because the personal foul was followed by a technical foul, both fouls must be penalized. The third foul in the sequence (the second technical foul) must be enforced after the previous two fouls, because the previous fouls were enforced, making it a false double foul situation. The POI principle only applies to true double foul situations or simultaneous foul situations under NFHS rules.
Disclaimer: POI also applies to other situations, such as inadvertent whistles, simultaneous free throw violations, and correctable errors. However my previous paragraph only mentioned foul situations.
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