Can two of your own pieces be pinned to your general at the same time?
These answers restate the rules implemented by our open-source engine, which follows the WXF laws for movement, checkmate and both repetition rulings: a side that forces a repetition by perpetual check or perpetual chase loses rather than drawing. The chase half has not been validated against the official casebook. Where an answer refers to a specific position, that position lives on the linked reference page, where the build verifies it before publishing.
Direct answer
Yes, easily. There is no rule limiting how many of your pieces can be pinned simultaneously. It is entirely possible to have one piece pinned on the central file by the flying-general rule while a completely different piece is pinned along another line by an enemy chariot or cannon, each pin working independently of the other.
Why this is dangerous
Multiple simultaneous pins usually mean a position has already gone badly wrong for the pinned side. Each pinned piece is a piece that cannot help solve the other problem, so a defender juggling two pins at once frequently runs out of useful moves before either pin can be broken.
Untangling one pin at a time
Pins are broken independently: moving your own general off the flying-general file does nothing for a piece pinned by an enemy chariot elsewhere, and vice versa. Work out which pin is actually costing you material or tempo right now, and free that one first rather than trying to solve both with a single move.
Related questions
Can one single move break both pins?
Rarely. A general step changes only its file or only its rank, so one step cannot break both a central-file pin and a pin along the general's rank; usually each pin needs a move of its own.
Is a doubly pinned position always losing?
Not automatically, but it is a serious warning sign worth calculating carefully before continuing.