Can you choose not to untap a permanent you control during your untap step?

By default, the untap step requires you to untap all permanents you control. CR 502.3 states that the active player untaps all tapped permanents they control. This is not optional — there is no general rule allowing a player to choose to leave their permanents tapped during the untap step.

However, there are specific card effects and rules that create exceptions. Some permanents say they 'don't untap during your untap step' (a restriction), and some others say 'you may choose not to untap [this permanent] during your untap step' (an explicit permission to skip untapping). Without such text, you cannot voluntarily keep a permanent tapped.

Phase actions like the untap step also cannot be responded to with instants or activated abilities — they simply happen (CR 502.4). There is no priority given during the untap step, so there's no window to make choices unless a card explicitly grants one.

Concrete example: You control a Prodigal Pyromancer that is tapped. At the start of your untap step, you cannot decide to leave it tapped to 'save' it from effects — it automatically untaps per CR 502.3. Contrast this with Stasis, which explicitly says permanents don't untap, overriding the default rule.

In summary: you must untap all your tapped permanents unless a card effect specifically says otherwise (e.g., 'you may choose not to untap' or 'does not untap during your untap step').