A map of English modal verbs, organised by what you're trying to do.

Present ability — what you can do now.

Past general ability — what you could do over a period.

A specific past success — the one time you pulled it off.

A success that took effort — you got there despite difficulty.

Fills the tenses can and could can't reach — future, perfect, after a modal.

Direct — asking or giving permission plainly.

A more polite way to ask — but it can't grant.

The formal register — 'May I', 'you may', 'may not'.

Very formal and now rare — 'Might I'.

Refusing permission — informally or firmly.

A real but low possibility — it may or may not happen.

Much like might, a touch more formal and a shade more likely.

Possibility — one of the things that's conceivable or on the table.

Probability — what you expect to happen, though it's not guaranteed.

Near-certainty in the negative — it almost surely isn't so.

A recommendation — the right thing to do, but not forced.

Much like should, with a slightly more formal, moral weight.

Practical necessity — required to reach the outcome.

Strong obligation imposed from outside — rules, circumstances, other people.

The strongest — your own authority, or a written rule.

The softest steer — offering an option, not even pressing it.

The standard recommendation — what you'd advise.

Like should, with a little more formal or moral weight.

Strong advice with a warning built in — do this, or there's a cost.

When advice tips into telling them it's necessary.

Direct. Assumes a yes. Right with peers and your own team; can read as blunt upward or with clients.

A small softening. Still direct, but adds a touch of politeness.

Frames the ask as a willingness check, not a capability check.

Asks permission to impose. Acknowledges the other person's time.

Maximum deference. Frames the ask as a tentative thought.

'We could…' — floats one option, no pressure.

'How about…?' — a casual idea on the table.

A friendly nudge toward an idea.

'Shall I…?' offers; 'Shall we…?' suggests.

'Let's…' — proposes and assumes you're in.

A tentative read — one possible explanation among others.

A possible explanation — on the table, not settled.

Possible, a touch more formal than might.

A confident positive conclusion — it almost has to be so.

A confident negative conclusion — it almost surely isn't so.

Past habits and states that aren't true now.

Repeated past actions — but not past states.

A present, characteristic habit — 'she'll always…'.

Accustomed to something — a present state.

Becoming accustomed — the process of adjusting.