Can the present perfect continuous construct be used in passive voice?

Solution 1:

I think "has been being built" is grammatical, but few people would say it. I think most people would use the impersonal active form you gave.

An alternative in some dialects is "This house has been a-building for years", but that's not in any standard variety as far as I know.

Solution 2:

Yes, the passive past perfect continuous is sometimes cited as being a relatively recent innovation in English (cf Mair & Leech, "Current Changes in English Syntax" in The Handbook of English Linguistics, Blackwell, p. 320) and isn't so common, though possibly on the rise. A similar observation is made about some other passive constructions, e.g. modal continuous passives ("would be being built").

Solution 3:

This house has been being built for years

is horribly clumsy and inelegant.

If I google the expression "has been being built", at my time/space coordinates it currently achieves 24,400 hits.

That figure seems to place this particular "has been being [X]" construction towards the upper end of the prevalence scale: if I substitute almost any other common verb for built, I get far less hits, e.g. eaten (82), drunk (11), got (18), gotten (8), forgotten (27), walked (21), run (89), cooked (40), fried (6), infected (11), cured (13), thought (14), read (77), spoken (31), written (7,600 - all the top hits here discussing whether the usage is allowable), performed (96), planted (15), grown (29), investigated (87), inspected (5), ridden (58), driven (63), cried (6), prayed (16), fucked (11), beaten (29), hunted (21), killed (21), buried (18), prohibited (1), encouraged (12), and questioned (32).

It should be noted that as with written, a fair number of the top hits for some of the other verbs related to the question of how grammatical such a construction is. So it is arguable that they should really be excluded from the counts on the grounds that they represent mentions rather than uses of the terms in question.

The most notable exceptions I found were said (a remarkable 4,260,000 hits), asked (1,175,000), and published (603,000). Done gets 29,700 hits.

The discrepancy between the semantically similar said (4,260,000) and spoken (31) cries out for an explanation, as does that for asked (1,175,000) and questioned (32); unfortunately, I don't have one.

Notwithstanding the above-mentioned outliers, it seems apparent that the "has been being [X]" construction is used little with most verbs.

The underlying idea embedded in your question is much more nicely expressed by your other variant,

They have been building this house for years

or by a form of words that uses a deverbal noun, e.g.

This house has been under construction for years

Alternatively, you can say

The {construction / building} of this house has been underway for years