this increases the handling current?
Yes, but it brings complications. The diodes would need to be in close thermal contact so that one couldn't get hot independently of the other (or it would "steal" current, get hotter yet, steal more current, then end up carrying the whole load).
Wouldn't (also?) drop more volts?
No, parts in parallel don't drop a higher voltage.
Why it uses double diodes?
Mostly you would do that if you couldn't get individual diodes that would carry the rated current, or if such diodes would be more expensive than diodes in parallel.
Which makes me wonder how old the book was, or how high a current the bridge was designed for. This was something that wasn't uncommon in projects from the 1970's (as I recall), but whose popularity was fading fast by the 1980's, even in amateur use.