I do wonder if we might have seen this in te twentieth century had there been no world war and Russian revolution.
I doubt it (if you are talking about a strict
male successions): there were not too many potentially available thrones in Europe and, as far as I can tell, even in the XIX century the Romanovs were not into putting their males on the vacant thrones (not too many of which had been available to start with). In other words, the "restrictions" (strictly males and the thrones separated from Russian Empire) introduced somewhere in a middle of a discussion should be disregarded if you want some realistic results.
The realistic openings for the narrow scenario (with a considerable stretch of imagination but without the ASBs):
1. Peter Ulrich (son of Anna Petrovna so, while his descendants are referenced as the "Romanovs" they are actually Holstein-Gottorp-Romanovs) inherits BOTH Russian and Swedish thrones (the Swedes at that time were under strong Russian influence so skipping the religious requirement is unlikely but not completely impossible). As a result, Sweden and Russia are in a personal union. Then either Peter III has 2 sons or split of the crowns happens after the death of Paul I (unlikely but not impossible).
2. As a result of either 1st or 2nd war with the Ottomans Catherine manages to carve some meaningful peace of the territory in Greece or Bulgaria while the Ottomans are defeated thoroughly enough to acknowledge independence of this territory (possible with some realistic changes). "Idiot's dream" comes true, there is a new "Byzantine Empire" and Catherine's grandson Constantine is a king/emperor of it.
3. When, during certain misunderstanding with their colonies in North America, the Brits are asking Catherine to lend them some troops in exchange of Majorca, Catherine agrees and makes Majorca an independent kingdom with, again, Constantine as a king. Anybody can speculate on the survival chances of this kingdom but, with the Brits and Russians being friendly most of that period, I'd say that they are higher than zero and later you have an established dynasty, legitimacy, etc.
4. Russia may try to negotiate the throne of newly-independent Greece for Russian Grand Duke (unlikely) instead of Otto of Bavaria,
5. As a result of the war of 1877 - 78 Russia may try to negotiate position of the Prince of Bulgaria for one of the brothers of Alexander II (preferably, Konstantine Nikolaevich to save Russia from his "activities"

) instead of Alexander of Battenberg. Not likely but if Russia is not trying to renege on its pre-war obligations, then there is no international isolation and probably German support is available (his mother was daughter of Frederick William III of Prussia). Not very likely but non-zero chance.
6. Seriously fantastic but still no ASBs: in 1848 Nicholas I supports Hungarians against Austria with a resulting Hungarian independence. Constitutional monarchy with one of Nicholas' sons as a king. Of course, this would require something like Nicholas being struck on a head with a really hard rock which would result in the improved mental capacities.
7. As further development of #6, Czechia, inspired by the Hungarian success, also revolts and you have one more throne available.
8. In 1795, the last Duke,
Peter von Biron, ceded the Duchy to the
Russian Empire. Unlike OTL, Catherine II made it independent state ruled by her grandson.