The most basic ones would include:
- actively, currently carrying out an action ((with much|with some|without] physical exertion)
- recently having finished carrying out an action (with|without physical exertion)
- intending to carry out an action (with|without physical exertion)
- being obliged to carry out an action
The participles can be used as adjectives, as nouns describing the state (with some syntactic restrictions on how they can be used), and as complements of some auxiliaries. Adverbial use is also possible.
Secondary idea that goes well: some auxiliary-like verbs lacking finite forms altogether, and being used for somewhat anaphora-like uses and in some idioms.
I envision this as being in a language with a relatively small nominal morphology, with a simple TAM system.