I'm looking for literature about IRT models that fit for tests in which items are presented for each examinee more than once and/or different questions are asked for the same item. For example, in the test the item "2+2" is shown twice, first when the examinee answers what is the equation sum and again when the examinee answers how many even numbers are in the equation. Or, in the test the examinee asked to rate for a picture valance and then asked to rate the picture's arousal (arousal and valence are orthogonal). Thus, the picture (the item) is shown twice but different aspects of the item are measured.
I'd be grateful for any direction and help.