The underlying issue is one of focus. Where is the perfective meaning inherent in the auxiliary verb have being focused? In (1) the liking is now and the studying is some time in the past. In (2) the liking is some time in the past (and thus the study). In (3) both the liking and the study are in the past.
Because, by implication, the study is in the past in (2), usage guides have taken against (3), on the grounds that it's unnecessary. Fowler, for example, was against it. In his article on the 'perfective infinitive' (in A Dictionary of Modern English Usage), we see him arguing that because 'the implication of non-fulfilment [is] inherent in the governing verb itself', examples like (3) are to be avoided. He adds:
'Sometimes a writer, dimly aware that "would have liked to have done" is usually wrong, is yet so fascinated by the perfect infinitive that he clings to it at all costs, & alters instead the part of his sentence that was right.'
He gives as an example: 'He would like to have insisted' and corrects this to 'He would have liked to insist'.
Note the 'usually'. A lot depends on the context. If this is unequivocally past time, then it makes sense for the pastness to be focused on the governing verb, otherwise there's an awkward or impossible sequence of tenses.
John used to work as a bouncer at the club for a low wage. He would have liked to be paid more, but...
not
John used to work as a bouncer at the club for a low wage. He would like to be paid more, but...
or
John used to work as a bouncer at the club for a low wage. He would like to have been paid more, but...
However, if the context begins in the present time, and later switches into the past, then we might indeed hear:
John is working as a bouncer at the club for a low wage. He would like to have been paid more, but it was all he could get at the time...
We can feel the speaker's focus shifting from one time-frame to another, and dragging the 'have' along with it. I've talked about this sort of thing before on this blog (eg with sentences like 'I've seen him three weeks ago').
Such sentences are thus more likely to be encountered in speech than in writing. They show some of the characteristics of a blend. In writing, Fowler's recommendation is usually followed by other style guides. But why is the 'double have' construction 'wrong'? I see a place for (3), if the writer wants the perfective aspect of both the liking and the studying to be emphasised. It's a bit like using a repeated negation. The two uses of nor are omissible in the following example, but it's easy to think of contexts where the emphasis would be desirable.
John doesn't like broccoli, nor cauliflower, nor beetroot.
It's less obvious in the case of would have, but the principle is the same.
