Probably not for a few reasons, it's basicly a completely different amp. You won't be able to make it sound like a Cobra but you could probably get a pretty decent metal tone that's 'like' a Cobra, if that makes sense? Cobra's are also proffesional grade high end amps.
Well, two things to be considered are that firstly it's a solid state amp, which will probably sound completely different to the Framus which is a vavlve head. Also, the Cobra is a head, the Crate is a combo, so they'll sound very different.
There's not much in the way of upgrading solid state amps as there's no valves (That's the most common 'upgrade' people do to change sound though it's not really an upgrade)
Sometihng like a Tubescreamer by Ibanez or a Digitech Bad Monkey, Boss SD-1 etc etc are all low gain overdrive pedals that people chuck infront of amps to tighten up low end and 'push' the amp. loads of Peavey/Mesa/Framus/etc guys do this, it's great. but that's usually for valve amps, solid state amps don't react as well to boosts. in front or effects loop EQ pedals like the MXR or Boss are good for tone shaping.
If you're keen on upgrading you could consider what alot of people do and buy a multi effects processor like a POD and run it through the clean channel of the amp, that's what I did with my old amp before I got a 5150, but that involves a fair bit of money and makes the whole 3 channel amp thing completely redundant haha.
You COULD also change the speakers, that would make it sound better but It's a waste of time and money.
In short, get a better amp, if you can't afford one or don't want one then just tweak the hell out of your current amp, I've sat with my amps before for a good while to get true awesome tone out of it, same with effects and evrything, Every single parameter effects tone, even Gain/Volume ratios. Seriously. Peavey 5150s and 6505s, specifically the II/+ series are what Cobras are often compared to, and they're pretty cheap on Ebay. They come in a combo version too which I hear sounds better and saves you buying a cab, also it's half the wattage so better tone at bedroom/small club levels. (I own the head, never played the combo)