The car wouldn't be heavy enough, even with a heavier and more powerful engine.
Looking at the Mitsubishi website a Shogun weighs 3000 kg and has a braked towing limit of 3500kg, it's an absolute monster
Looking at new Caravans you are limited to Freedom or Elddis Xplore, I guess.
Anything over 1000 kg will exceed 85% of the cars weight which is not recommended.
Some cars are specced upto 100% of kerbweight in the handbook e.g. Nissan Juke, Renault Megane. FIATs don't have high handbook tow specs and you should also consider, say, 85% of spec instead of kerbweight, to be conservative. Maybe it says 1100kg in the handbook, I wouldn't want to tow that.. that's the safe LIMIT.
It's not just the engine power and car weight, you also have the max nose weight on the ball and the weight of the back of the car. If the back of the car is heavier you improve the stability i.e. helps stop snaking, which is part of the reason why 4x4 have higher spec tow weight (you notice this if the car has 2wd and 4wd versions available with the same engine and similar bhp). Yes modern stabilisers have almost eliminated snaking but you do feel, say, the wind effect you less in a higher specced car even if the car isn't heavier and the engine no more powerful. The handbook spec also takes into account other factors like the strength of the tow mount I suppose.
etc. etc..
In conclusion don't buy any 1200kg car for towing anything but the lightest type of caravans and have a good outfit match of 85% kerbweight or handbook spec, whichever is lower.
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