You ask if it is possible to measure 'Multiple intelligences' through self reports. I think that your question has to do with Howard Gardner' theory of multiple intelligences, that is, linguistic intelligence, logical-mathematical intelligence, musical intelligence, spatial intelligence, bodily-kinesthetic intelligence, interpersonal intelligence and intrapersonal intelligence. As you certainly know, Gardner's definition of intelligence is one's ability to solve problems or to create products that are valued within one or more cultural settings.
Let me say, that I always looked at Gardner's multiple intelligences with some caution. For example, why is there a spatial intelligence but not also a temporal intelligence? If objects exist in a certain space, events always occur at a certain time. And one can be intelligent without create products. So, I prefer J. Piaget' or S. Hawkins' definition of intelligence as one's ability to actively adapt to change to Howard's definition of intelligence.
As for your main question, you might raise it to Howard Gardner. He certainly will give you an appropriate answer.
I attach to my answer a PDF file I Find in the Net. The file speaks about the measurement of multiple intelligences. It can be the case that the file is of some help for you.
Tirri, K., Nokelainen, P., & Komulainen, E. (2013). Multiple intelligences: Can they be measured?. Psychological Test and Assessment Modeling, 55(4), 438.