In an interesting opinion regarding dominant/servient jurisdiction and abatement, the Houston (First) Court of Appeals made this observation regarding the proper relief on a motion to abate:
Generally, the proper relief on a motion to abate on the ground of dominant jurisdiction is abatement. . . . However, there is also authority that that if a party files a plea in abatement . . . the subsequent case must be dismissed. The Texas Supreme Court has noted the split in authority , but has not resolved it.
Here, the trial court dismissed the case, but the court of appeals did not have to address the proper remedy because the plaintiff did not challenge the dismissal.
I wonder whether this quandry can be resolved by analyzing whether the claims asserted in the subsequent lawuit can and should have been asserted in the first suit. In other words, the answer may depend on whether res judicata would apply in the subsequent lawuit. If so, then dismissal may be proper if for no other reason than to require the plaintiff to bring the claims in one suit. The court of appeals’ opinion in French v. Gilbert can be found at this link.