"There appears to be" or "There appear to be" + plural noun phrase

Solution 1:

"There" indicates the location of the missing functional system. Adverbs can indicate the place of the action of the verb. Accordingly, "there" is an adverb modifying the verb "appear." The sentence has an un-necessary plural form of "system." It is (logically) more concise to say "no system" (as in not even one system) instead of "no systems."

The sentence should be re-written "There appears to be no functional system in place to handle this." Where the subject is "no functional system" and the verb is "appears."

An alternative, equivalent, form of the sentence in more conventional subject-verb order would be "No functional system appears to be in place to handle this, there."