When grinding out many (practising!) 'harmonising 4 part' exercises for my Music Theorey Exams, I noticed that my teacher managed to get me to (mostly) avoid parallel thirds by suggesting that I use one of the other notes from the particular chord being used at that point. If that did not produce satisfactory results, then to think about a modulation around that section. This was mainly intended for 4 part vocal harmony, and the intention was to produce 'singable melodies' for all the parts - it's relatively easy to grind out 'Mr Bassman' type lines as per certain popular musical genres... :-P

It also ignores the question of easily producing 'vamping style' accompaniment, as per certain other popular musical genres...

Of course, there is quite a difference between just 'grinding out' this sort of random garbage on paper, and extemporising live on an instrument to obtain 'real music' ... :-)