I cannot find a Sutta that says that one has to exit the current Jhana he is in and find himself outside the Jhana realm then re-enter with the intention to go to another Jhana and slide through the ones before and until the one he wants to go to.
This comes close:
Then the Gracious One attained the first absorption, and after emerging from the first absorption he attained the second absorption, and after emerging from the second absorption he attained the third absorption, and after emerging from the third absorption he attained the fourth absorption, and after emerging from the fourth absorption he attained the sphere of endless space, and after emerging from the sphere of endless space he attained the sphere of endless consciousness, and after emerging from the sphere of endless consciousness he attained the sphere of nothingness, and after emerging from the sphere of nothingness, he attained the sphere of neither-perception-nor-non-perception, and after emerging from the sphere of neither-perception-nor-non-perception, he attained the cessation of perception and feeling. (DN 16)
But it doesn’t speak of “exiting current jhana, finding oneslef outside jhana realm and re-entering higher jhana”.
It a quite specific ‘request’ to the suttas, but I guess the question is if the 2nd needs a special new intention? I am careful with single suttas, but is AN 9.35 satisfactory?
there are cases where a monk—foolish, inexperienced, unfamiliar with his pasture, unskilled in being quite withdrawn from sensuality, withdrawn from unskillful qualities, and entering & remaining in the first jhana: rapture & pleasure born from withdrawal, accompanied by directed thought & evaluation—doesn’t stick with that theme, doesn’t develop it, pursue it, or establish himself firmly in it. The thought occurs to him, ‘What if I, with the stilling of directed thoughts & evaluations, were to enter & remain in the second jhana: rapture & pleasure born of composure, unification of awareness free from directed thought & evaluation—internal assurance.’ He is not able… to enter & remain in the second jhana… The thought occurs to him, ‘What if I… were to enter & remain in the first jhana… He is not able… to enter & remain in the first jhana. This is called a monk who has slipped & fallen from both sides, like the mountain cow, foolish, inexperienced, unfamiliar with her pasture, unskilled in roaming on rugged mountains.
Also AN 9:41
Then, Ānanda, it occurred to me: ‘With the subsiding of thought and examination, let me enter and dwell in the second jhāna. . . .’ Yet my mind did not launch out upon the absence of thought and become placid, settled, and liberated in it, though I saw it as peaceful. It occurred to me: ‘Why is it that my mind does not launch out upon the absence of thought and become placid, settled, and liberated in it, though I see it as peaceful?’ Then it occurred to me: ‘I have not seen the danger in thoughts and have not cultivated that [insight]; I have not achieved the
benefit in the absence of thought and have not pursued it.