To make a Computerized Adaptive Test out of a sample of 20 dichotomous items a typical course of action would be to:
1) calibrate respondent data with a R package like mirt or ltm using Rasch, 2PL etc.
2) create an itembank based on obtained item parameters using catR
then, for each item/test taken:
3) use catR's nextItem function and method (e.g. MFI) for selecting a next item based on previous items and answers
4) choose a stopping rule, e.g. stop if SEM < 0.2.
5) use last theta and SEM as 'test results'
However, regarding polytomous items and multidimensional tests I'm a bit confused. For a polytomous, multidimensional CAT, e.g. 100 items (5 scales) of a personality test with a 5-point-likert scale, the test logic, item parameters (GRM/GPCM) and item selection are very different.
Specific question: is there a polytomous version of catR's nextItem function available?
Broader question: What methods/packages/steps would you recommend for making a working polytomous CAT with MIRT?