If there is a character in the beer you like, check out "Brew Like a Monk" by Stan Hieronymus. Great table in this book about the various Belgian yeast strains from both major liquid yeast companies, and the characters they produce at various fermentation temps.
Not much in the book about La Trappe/Konigshoeven. An interesting side note is that Chimay once contracted with Konigshoeven to brew their white. warning that this is complete speculation on my part, but could they be using the Chimay yeast?
You could also try culturing the yeast as others suggested, but if there is a specific character you are seeking, the conditions of fermentation can make a different beer with the same yeast. Therefore, time spent with BLAM could be really helpful in this regard.