There's no way to get extra Pokemon on the same route. If there was it'd defeat the purpose of the one Pokemon per route rule.
Also, shinies do not count as an extra catchable Pokemon on the same route. If you've caught, beaten or run away from the first Pokemon of a route, that's basically it. No more Pokemon can be caught for that route. The exception to this is before you first have Poke Balls and if you follow the optional rule of having two more tries at catching a single Pokemon should you faint or run away from the first.