With a POD of 1940, is it plausible for Salazar to follow in Franco's footsteps this way?
no, because Salazar had no control over the country for the last two years of his life and Portugal had been a republic since 1910, 60 years before Salazar's death
POD would be 1940, like OP stated. And I understand so that Salazar would make Duarte his successor like Franco did so Duarte would ascend to Portuguese throne after Salazar's death/resignation.
Assuming a figurehead king is around when Salazar dies, if he is capable of forcing a liberalisation of the Estado Novo, an inevitable revolution would likely force him out, either during said revolution, or through a later referendum or Parliament vote.
I miswrote my sentence. I meant:Duarte as king would lead only to a violent republican restoration similar to the Carnation Revolution IOTL, as Duarte was the claimant for the Miguelist faction in Portuguese Monarchism which advocated for total unflinching absolutism as they were basically Portuguese Carlists.
A free referendum during the dictatorship would not be the best option to restore the monarchy, since Monarchism was minoritary and was discredited since 1890 (and without much support when it fell in 1910).I'm a bit late responding here, but I had some thoughts. My understanding is that Salazar had toyed with the idea of restoring the monarchy during his tenure in power, but apparently the Portuguese Pretender, Duarte Nuno, was too optimistic in his aspirations for a restoration and thus Salazar feared for his own power, and quashed any restorationist talk. It's possible for Salazar to not learn of Duarte's ambitions and perhaps then he presses through restoration or perhaps a referendum on the issue. Posthumously though, I don't see it happening. By that point the regime was far too entrenched in Salazar's person, and he wasn't thinking in terms of what would happen after his death. The rest of the Estado Novo wouldn't have tried to do something as drastic as restoration, so that option is out too.