dgongs pa can bzhi
four ways of teaching by the Buddha, as his intention was grasped by others [IW]
the four types of statement bearing an ulterior intention: the four other intentions are 1) equality (mnyam pa nyid), 2) another time (dus gzhan), 3) other objects (don gzhan), and 4) the attitudes of specific people (gang zag gzhan) TBD with reference to bod rgya tshig mdzod chen mo
Discussion
This is a tricky word to translate as a non-tongue-twister in English. Basically these are four "other things that the Buddha was really 'thinking' (dgongs pa) about" when he taught them. It would be nice to have others' thoughts about what might be a more non-academic way of saying this.
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Here is a passage I once translated from Sogdokpa (Sog bzlog pa). If any of it helps you, make use of it, but then again, discard this message:
<<As examples of antidotal flexibly-intentional statements, the Buddha said, "I myself in those times became the Buddha Vipaśvī (Rnam par gzigs)." In this way He meant to point out the sameness of Dharmakāya. [This is the intention of indicating sameness.] Also, "If you serve Buddhas as many as the sands of the Ganges, you will hear these teachings." In such statements He had another purpose in mind [besides the plainly obvious one]. "Those who have made merit and make aspirations for Sukhāvatī will take birth there." Such statements have a different time-frame in mind [than what seems to be implied]. "Generosity is inferior, while discipline is supreme." This was expressed with the inclinations of the [particular] person in mind, the textual traditions and reasoning determining the course of the words and meaning [in the preceding cases].>>
Of course 'flexibly-intention[al]' translates ldem dgongs, or ldem po'i dgongs pa.
These categories were quite well known to Tibetans in Imperial Period, as you can see from Thubten K. Rikey & Andrew Ruskin, trs., A Manual of Key Buddhist Terms: Categorizations of Buddhist Terminology with Commentary, Library of Tibetan Works & Archives (Dharamsala 1992), pp. 91-93.
But perhaps all of this is too less non-academic? Actually, I think it's very important to keep the categories straight here, even if that might seem an academic thing to do. Besides, the question of 'intention' is a deeply perplexing one in philosophy, linguistic philosophy in particular. And the prospect of divining the Buddha's true intention in saying what He said is truly and deeply perplexing Buddhistically speaking. It deserves a lot more thought than I'm ready to give it at the moment.
Again, make use of any of this that can be made use of, then please do discard this bumbling discussion! I probably meant to say one thing, but ended up saying another.