The easy-to-remember rule is to place the adverb immediately before the word being modified.
Joe swiftly ran to the extremely bright red car.
Note that other positions may or may not mean the same thing:
Joe ran swiftly to the bright extremely red car.
Here ran swiftly means the same thing simply because swiftly could only modify an action verb.
The same is not true of reordering extremely and red: Now it means the car is considerably red (meaning intense or well covered) and no longer means it is significantly bright.
Other positions for adverbs are often acceptable. But if in doubt, beside the word being qualified is safe.
However, the only rule of English being that there are no absolute rules: fast is also an adverb meaning swiftly. So by the rule above, this should be fine:
Joe fast ran to ... (incorrect)
English speakers would only say Joe ran fast ... even though fast ran must mean the same thing. (I don't know why this is—only that it is so.)
To directly answer the question: Yes, you could put an adverb there, but it might not have the intended effect. Or it could be ambiguous or misleading.