You can only bring it what is in the .ai comp size. If you are not willing to edit the artboard size in illustrator then you have the following options.
1. Grab everything in illustrator and shrink the size so it all fits in the 1920 x 1080 area. It is vector so in illustrator you can increase the size with zero loss of quality. (But if that is the case you might as well just increase the artboard size in illustrator which is what I would do)
2. You can move the elements outside of the comp area and move them into it so you have vector images stacked on each other. Then you move them back into place in AE.
Stephen Smith
Utah Video Productions
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