I've already come across the question concerning what may follow break into:
break into (allowable complements)
The multi-word verb break into has various senses and takes various complements - but there are sense-dependent restrictions on the varieties and actual choice of the noun groups etc that may be put after the MWV. (I'm avoiding classification of the noun groups etc as, for instance, 'direct object' because there is no consensus on the grammar involved.)
First, let's disambiguate, as Wikipedia usually sensibly starts off by doing:
(0) The glass vase broke into a thousand pieces. isn't a usage of the multi-word verb - this is just break followed by a prepositional phrase.
Now, listing possible complements and senses for the MWV break into:
(1) count nouns (or nouns nearer the count end of the spectrum):
(a) (breaking and entry) The thieves broke into a / the bank.
(b) (rapid acceleration to high speed) The horse broke into a gallop.
(b') (sudden switch to more dashing activity) Fred and Ginger broke into a tango.
(c) (rapid switch to more feverish state) Ted broke into a sweat.
(2) non-count nouns (or nouns nearer the non-count end of the spectrum):
(a) (sudden start of an activity) They broke into song / applause. [though notice that broke into a song is also allowable]
(b) (to interrupt) No one would have dared to break into his abstraction.
(c) to enter (a field of activity / career) (a degree of difficulty having to be overcome): He eventually broke into journalism. [though notice that broke into a career in sculpting / journalism is also allowable]
However, there are further restrictions: (2a) would seem to license 'broke into singing', whereas the only meaning allowed for this clause is the (2c) sense, where 'singing' is a gerund and parallels 'acting' or 'banking'. 'Ted broke into knitting' is ridiculous. In fact, the number of nouns sense (2a) accepts is very small - even amongst semantically sensible ones.