I think you will struggle to add a third sector (such as BRU-AMS-CDG-JFK) on that routing. Beware that adding an extra leg on the US side counts for far fewer XPs (as it is a domestic sector).

I have seen the KLM website suggest ZWE(Antwerp Central Station)-AMS-MAN-JFK (the latter as a KL codeshare on Virgin Atlantic) but for prices well above more direct routings, making it an uneconomical way of getting just 5 extra XPs.

and note that adding sectors per se doesn't affect the number of miles. The mileage earning is based solely on the price paid; the price paid doesn't react directly to the number of sectors added. This is different to the XP earning, where each individual sector is considered when determining the XPs awarded.