(Please help) Imputing multiple Likert-type items

I have a set of Likert-type variables that I'm trying to sum up to form a scale. My dataset has around 5000 subjects, and there are about <10% subjects who have missing values on at least one item with an arbitrary missing patern. It's reasonable to assume that my data is missing at random. Now I'd like to make use of the correlation among this set of items to impute the missing. Can anyone suggest a good method?

I checked SAS PROC MI, and it seems like it mostly handles continuous variables. I see one example involving one binary variable plus a set of continuous variables. I don't see if SAS can handle a set of ordinal variables. I tried to treat my ordinal data as continuous, than I got imputed values out of range on both ends.

I read a paper that suggested "relative means substitution" method for likert-type of data. This would avoid the "value out-of-range" issue. But I also read somewhere that the method is out-dated. Besides, I'd prefer to have multiple imputations anyway.

Can anyone who's familiar with this topic pleae provide any suggestions? Your help is greatly appreciated.