Are predicateless auxiliaries iterable?

Hi! In many languages, auxiliaries are used to build periphrastic verb tenses. Some English examples from the English MRS Test Suite:

351 The dog is barking.
361 The dog has barked.
371 The dog has been barking.
381 The dog had been barking.

In order to learn how the customization questionnaire works, I implemented a small grammar fragment of English. In this fragment, I treated these helping verbs as auxiliaries without predicates. I seems that this analysis is quite common across different theoretical frameworks, e.g., LFG. The underlying assumption is that these verbs just contribute person, number, tense and mood features to the sentence. Frequently, these periphrastic constructions are rendered by affixes on the verb conveying the sentence’s main predicate. For example, sentence 361 is translated as follows in the Portuguese version of the test suite (my glosses):

O cão ladr-ou.
the dog bark-IND.PRF.3SG
‘the dog has barked’

In Portuguese, there are two ways of building the pluperfect: either synthetically or analytically:

O cão ladr-ara.
the dog bark-IND.PST.PRF.3SG
‘the dog had barked’

O cão tinha ladr-ado.
the dog have:IND.IMPF.3SG bark-PST.PTCP
‘the dog had barked’

With this implementation, however, the grammar didn’t analyse sentences with more than one auxiliary, although I had specified that multiples auxiliaries are allowed.
Accidentally, I discovered that auxiliaries can iterate if they are assigned a predicate in the questionnaire. In the Portuguese grammar I’m developing in collaboration with @arademaker, I have implemented modal verbs and some subject control verbs as auxiliaries with a predicate. In the test suite the grammar is being tested on, there are some examples with multiple verbs of this sort, e.g.:

o cachorro continua tentando perseguir o gato
the dog keep:IND.PRS.3SG try:PROG chase:INF the cat
‘the dog keeps trying to chase the dog’

The grammar parsed these sentences as expected. The sentences with multiple predicateless auxiliaries or with one auxiliariy of this sort and an auxiliary with a predicate, however, were not parsed, e.g.:

o cachorro está tentando perseguir o gato
the dog be:IND.PRS.3SG try:PROG chase:INF the cat
‘the dog is trying to chase the dog’

After I had re-implemented the progressive auxiliary estar ‘be’, the future auxiliary ir ‘will’ and the perfect auxiliary ter ‘have’ as auxiliaries with predicates, the grammar parsed such examples.
Was this behavior of the questionnaire as expected? Should auxiliaries without predicates be prevented from iterating or have I possibly done something wrong? Has anyone had a similar experience with the questionnaire?
I’m not convinced that the auxiliaries estar ‘be’, ir ‘will’ and ter ‘have’ contribute anything to the semantics of these sentence beyond the tense, mood, person and number features. But one can maybe treat their semantic contribution as a kind of dummy predicate.
By the way, I’m writing this as @leonel, which will be my profile henceforth instead of @leoalenc, which I used before.

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Hi Leonel,

I had a similar issue when I was modeling some languages in my dissertation (see page 320 as marked on the pdf).

I does appear that this is a limitation of the questionnaire.

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Thanks for the reply, @olzama, and for the PDF of your dissertation!