Klingt schon sehr merkwürdig, könnte aber theoretisch richtig sein.: Bis nächsten Dienstag werde ich deinen Aufsatz GElesen haben können.

Bis Mittwoch wird das Haus geputzt sein müssen, damit ...
Bis Mittwoch werden wir das Haus geputzt haben müssen, damit ...

For any Future II you need a past participle. Judex is right: "gelesen haben können".
For any passive voice you need a form of "sein" (Zustandspassiv) or "werden" (Vorgangspassiv) plus a past participle.
Your example "Das Haus wird geputzt werden haben müssen..." is not correct. It is das Haus wird geputzt sein müssen (Zustandspassiv) oder das Haus wird geputzt worden sein müssen (Vorgangspassiv). The latter is rather stilted, nobody would use it. Rather, people use the simple present for the modal verb: "Das Hotelzimmer muss bis 11 Uhr aufgeräumt sein".
Does that answer your question?

Thankyou for your replies...

Is "gelesen haben können" really the correct answer for the first sentence? I'll explain my train of thinking...

Consider the following:
"I won't be able to read your essay this week, but by next Tuesday I will have been able to."

I would render this as "...aber ich werde bis nächsten Dienstag gekonnt haben."

Here it is clear that the past participle is formed from the verb "können". It seems rather arbitary to me to say that because when we introduce another verb (lesen) and can no longer use "gekonnt" that we should therefore use "gelesen" instead of plain "lesen".

Hence the question - can one use modal verbs in Futur II when they don't stand alone but are, instead, used together with an infintive? Any further thoughts?

Many thanks,
Matthew

"gelesen haben können" is definitely correct. I don't quite see your problem with this construction. Like Sebastian wrote in #2, you need a past participle for any Futur II construction. In this case, it is "gelesen", in your other examples it is "geputzt" and "gekonnt", like you correctly wrote.

BTW I do ocasionally use stilted constructions like your "das Haus wird geputzt worden sein müssen", but I do agree with Sebastian that hardly anyone speaks like that and you would normally express it in a different way.

And while your "aber ich werde bis nächsten Dienstag gekonnt haben" is technically correct, apart from the fact that it should read "ich werde es gekonnt haben", most people would be more likely to say "aber ich schaffe es bis nächsten Dienstag".

Yes. And Matthew, if this still reaches you: The "es" in Dragon's correction is crucial -- "ich werde es gekonnt haben", for what is "es"? "Es" stands for "den Artikel gelesen haben".

The point is that you can technically use modal verbs as full verbs (können = to be able to), but in their function as modal qualifiers they are rather close to auxiliary verbs (können = can). The full verb which is modified by "können" is "to read/lesen" in your example. So you prefer inflecting the strong verb and keeping the modifier over inflecting the modal verb and leaving it unsaid what has been modified.

ich kann es -- ich werde es können -- ich werde es gekonnt haben (full verb)

ich lese den Artikel -- ich werde ihn lesen -- ich werde ihn gelesen haben (full verb)

ich kann den Artikel lesen -- ich werde ihn lesen können -- ich werde ihn gelesen haben können (full verb + modal verb)

The same is true for the passive voice, and even more strikingly so. For the full verb "werden" (= to become), there is a past participle "geworden":

Ich werde Bäcker -- ich werde Bäcker werden -- ich werde Bäcker geworden sein

The modal verb has no past participle. The passive voice is formed by past participle plus sein/werden. You can't say "*das Haus wird geputzt geworden sein*". So there is only one past participle in Futur II, the one demanded by the passive voice. Here is the "Vorgangspassiv" with "werden":

Das Haus wird geputzt (is currently being cleaned) -- das Haus wird geputzt werden -- das Haus wird geputzt worden sein

And now with an additional "müssen":

Das Haus muss geputzt werden (the house is not being cleaned, but we recognize the necessity) -- das Haus wird geputzt werden müssen -- das Haus wird geputzt worden sein müssen

So I think the main part of your problem is to decide whether "werden" is an auxiliary verb as in regular tenses like Futur I ("ich werde kommen") or a modal verb showing a process under way ("die Straße wird gerade geteert") or a full verb ("Ich werde gerade zum Experten in Grammatikfragen!").

As a rule of thumb, I'd advise that you use the main activity you are talking about as the full verb, which then carries the whole load of inflection, and subordinate all modal or auxiliary verbs. This is why "ich werde den Artikel bis Dienstag gelesen haben können" is idiomatic, while " es (= ihn gelesen) gekonnt haben" is not.

All this said, your example, "I won't be able to read your essay this week, but by next Tuesday I will have been able to", is somewhat marred by the fact that you use a full verb in English but demand a modal verb (können) in German. One proper translation would be, "ich werde deinen Aufsatz diese Woche nicht [ mehr ] lesen können, aber bis Dienstag werde ich ihn [ sicher ] gelesen haben [können ]." If you use "sicher", this has the same modal function as "können", so you don't need both. But you asked for the correct use of modal verbs in Futur II, so alternatives without the modal verb (dragon's solution is another good solution) don't really interest you, do they?

Does this make anything clear or are you now completely lost like Mark Twain was when he advised American users of German to attach something like "gehabt zu haben zu sein" to any German sentence?

BTW, @ dragon: Yes, I like complicated or rare structures, too, in German as well as in English, and I sometimes use them malevolently. I simply love this dazed look on the faces of people who try to digest what you said word by word, hoping to ascertain on the way if you are trying to fool them or if they missed something in their education. Sorry for that.

Sebastian - many thanks for taking the time to write such an exhaustive answer. I will read, try to digest and hopefully be the wiser for it - thanks!
Matthew

I would like to add a thought to this issue. For me, the main question is: How does the verb system of a certain language solve the problem of comunicating the intended information?

On the basis of the classification developed by Latin grammarians, verbs provide us with 5 pieces of information.
- Person (1st, 2nd, 3rd)
- Numerus (i.e. singular or plural)
- Tense (present , present progrssive, past perfect, futur perfect, for example)
- Genus verbi (active voice or passive voice)
- Modus (Indikativ, Konjunktiv, Imperativ)

Example: "es wird geputzt worden sein" = "it will have been cleaned" =
- 3rd person
- sg.
- futur II (future perfect)
- passive voice
- indicative mode

Now, when we would like to modify a certain "main verb" (e.g. "clean"/"putzen") with a modal verb ("can"/"koennen", "must"/"muessen), this classification leads to the question of whether the 5 pieces of information mentioned above are provided by means of inflecting the modal verb or the main verb (or a combination thereof).

English and German HAVE FOUND DIFFERENT ANSWERS to this question.

Let's first have a look at how the English language addresses this problem.

a) ENGLISH:
1st person sg futurII active indicative, main verb: read, modifier: can/be able to
- "I will have been able to read."
3rd person sg futurII passive indicative, main verb: clean, modifier: must/have to
- "It will have had to be cleaned."

In the English case, the modal verbs "can/be able to" and "must/have to" carry the information about person, number, tense and mode.
The main verbs "read"/"clean" are added as infinitives ("read"/"be cleaned") and provide us with the information about the Genus verbi (active/passive voice).

b) German
1st person sg futurII active indicative, main verb: lesen, modifier: koennen
- "Ich werde gelesen haben koennen."
3rd person sg futurII passive indicative, main verb: putzen, modifier: muessen
- "Es wird geputzt worden sein muessen."

In the German case, it is the main verbs that carry ALL the information about person, number, tense, active/passive voice and mode.
The modal verbs are always added as plain infinitives (active voice).

In sum: My point is that we can avoid a lot of confusion if we take into account that English and German use different strategies to convey the 5 pieces of essential information to the reader, namely by distributing the information between the main verb and the modal verb in a different way.