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

When faced with a situation like this, I recast the sentence in my head to better understand it:

There do not appear to be [any] functional systems in place to handle this.

So I agree that appear is correct. I greatly appreciate the discussion this created, because my gut/instinct/experience said that appear was correct, but it's nice to have evidence to cite if asked.

There appears to be no functional system in place to handle this. There appear to be no functional systems in place to handle this. I think this is correct because you can rearrange the sentences to: "No functional system appears to be in place to handle this" and "No functional systems appear to be in place to handle this". Functional system(s) is the subject in both sentences because you can get rid of "There" in the first sentence without altering its meaning. I used subject-verb agreement to pair the singular noun "system" with the singular verb "appears" in the first sentence, and I also paired the plural noun "systems" with the plural verb "appear" in the second sentence.

"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."

2. There appear to be no functional systems in place to handle this.

This is correct.

We can see that "there" is not a noun in

"There is a dog in the garden" -> "There are two dogs in the garden."

There is not a noun phrase. It is an adverb. There appears in two forms:

Locative/demonstrative - Your pen is there = in/at that place

Existential: "There are pens in the cupboard. This is the weakened form and merely indicates the existence of the subject of the verb - "pens".

In "There appear to be no functional systems in place to handle this." The subject is "no functional systems", which is plural. The verb thus agrees with the subject = appear.

We can rewrite as "No functional systems appear to be in place to handle this."

The interesting point is if an adverb fronts a sentence the subject-verb order could be inverted, e.g. "Dearly did I love her."

In modern English this is now mainly restricted to locatives: "Here are your pens and there is the paper!"

OED:

I. As a demonstrative adverb.

• Expressing locality or position.

1.a. In or at that place; in the place (country, region, etc.) pointed to, indicated, or referred to, and away from the speaker; the opposite of here.

1850 J. McCosh Method Divine Govt. (ed. 2) ii. i. 142 Wherever we find law, there we see the certain traces of a lawgiver.

and

4. Used unemphatically [...] the verb comes before its subject,[...] The same order was formerly observed after an introductory adverb or clause, [...] Grammatically, there is no difference between There comes the train! and There comes a time when, etc.; but, [...] in the latter it has been reduced to a mere anticipative element occupying the place of the subject which comes later.

Preceding or following a main verb, or following any verb, there, thus used, is stressless [...], but preceding be or an auxiliary, there has a slight stress, and the verb is enclitic (e.g. ˈthere-is, ˈthere-was, ˈthere-will).

1857 H. T. Buckle Hist. Civilisation Eng. I. vii. 399 From all these things there resulted consequences of vast importance.

4 d. especially with the verb to be: cf. be v. 1b, 4b there is, there are, are equivalent to French il est, il y a, German es ist, es sind, es gibt, Spanish hay. [...]

1608 W. Shakespeare King Lear vii. 459 For many miles about ther's not a bush.