Can the gifted companions from Ex Miscellania create breakthroughs to expand their powers? For example can a beast master learn to gain a animal familiar , or a sahir to gain a jinn spirit familiar?
Salvete Sodales!
It is possible - but comparatively hard!
Actually that is true IT and OT. OT the problem is that there isn't much to go on except a short passage in the general chapter of HMRE. Unless your troupe is fine with handwaving details there will be a hell of work to do in order to fix the mechanics.
IT the tradition needs a magic theory of its own in oder for its practicioners to be able to pursue further breakthroughs. Lacking this prerequisite, the only option is to develop one, and that's comparable to a hermetic breakthrough. Furthermore, even those hedgies with theories of their own aren't as likely to acchieve breaktroughs as their hermetic counterparts, they need twice as many breakthrough points.
They only good thing for ExMisc hedgie-researchers is the comparatively easy access to vast amounts of source material for insights, at least as long as they try to integrate some aspects of standard hermetic theory into their system.
Btw, they examples you are listing aren't actually Gifted companions but hermetic traditions with some remnants of their predecessors' non-hermetic past.
Vale,
Alexios ex Miscellanea
Yes they can, but if you are using the breakthrough mechanics you will need a magic theory of your own hedge tradition.
Another option would be go the way of Initiations into Mysteries. I am fairly sure that spirits of the magic realm can initiate new virtues for you, for example, so there you have quests to get the virtues 
Legends of hermes has a good chapter on that line of thought in the island of spirits chapter.
Xavi