Update 17 01 2023 my article on Articles 33-34 has now been published: Lis Pendens and third states: the origin, DNA and early case-law on Articles 33 and 34 of the Brussels Ia Regulation and its “forum non conveniens-light” rules, The link in the title should give free access to the first 50 takers, and I assume link to the review for those that come after.
Peter Ola Blomqvist v Zavarco PLC  EWHC 1898 (Ch) is to my knowledge the first serious consideration of the new lis alibi pendens and related actions provisions of Articles 33-34 Brussels I Recast.
The defendant company has applied for a stay on the basis of forum non conveniens and/or lis alibi pendens founded on the pendency of the action in Kuala Lumpur.
Donaldson DJ first considers whether claimant’s action falls within Article 24(2)’s exclusive jurisdictional rule for company matters. Article 34 has no application where jurisdiction is assigned by Article 24.
Precedent referred to includes Reichert as well as BVG. The claim founds on the claimant, Mr Blomqvist’s allegation that the company has failed to comply with its obligation under applicable English corporate law to call a meeting at the request of a member registered as the holder of more than 5% of the paid-up shares so as to enable consideration of resolutions to replace the directors, thus entitling him to convene such a meeting himself. The company contests that the court is obliged to focus on the defence that the shares were not paid up, which he suggests is the only real matter in dispute and turns solely on whether the terms of the relevant purchase agreement were complied with, a matter outside Article 24.
At 25: CJEU Case-law and the Jenard report exclude ‘from the reach of Article 24 a contractual claim to which questions of corporate governance were advanced by way of defence. It is however equally important not to remove from its ambit a claim seeking redress for failures of corporate governance on the basis of a defence which is purely contractual.’
Turning then to Article 34. Donaldson DJ suggests at 34 that ‘The clear purpose of Article 34 is to liberate the court from the constraint imposed by the Regulation in earlier versions, exemplified in Owusu , as regards stay in favour of the courts of non-Member States.’ I am not convinced. Articles 33-34 may now allow for a stay in relations with third States. Yet forum non conveniens is one thing – and indeed one ruled out by the CJEU under the Brussels regime. Articles 33-34 are quite another.
Consideration is then made of the rather awkward first condition of Article 34 that a stay requires that ‘it is expedient to hear and determine the related actions together’. At 38: ’it is hard to see how the actions could in practice ever be heard and determined together and hence how such a course could ever be expedient. This result can, as I see it, only be avoided by a purposive construction which treats the words “is expedient” as equivalent to “would have been expedient”. I believe this is right: this condition is likely to have to be interpreted at an abstract level: as in that it would have been expedient to hear the actions together (typically, by use of Article 8(1)’s anchor mechanism), had the considerations involved competition between two (or more) EU courts: seeing as an EU judge is evidently in no position to demand a related action be handed over from a third State court.
The bar for the application of Article 34 is necessarily high – and was arguably applied so in Zavarco: at 41 ff convincing arguments are displayed to that effect.
Finally, at 44 ff Donaldson DJ entirely justifiably, and emphatically, rejects the suggestion that with lis alibi pendens having failed, a stay could be issued on case-management grounds: (the Owusu) prohibition cannot be circumvented by re-labelling the exercise as one of case management so as to “achieve by the back door a result against which the ECJ has locked the front door”(per Lewison J in Skype technologies SA v Joltid Ltd  EWHC 2783 (Ch) ).
This is the first proper consideration of Article 34 of the Recast. No doubt it will not be the last.
(Handbook of) European Private International Law – 2nd ed. 2016 (forthcoming), Chapter 2, Heading 126.96.36.199, Heading 188.8.131.52.