Hello and welcome to FT!

To be able to help you better:
1. How long are you staying away from BRU ?
2. Which class are you opting for - F/C/Y ?
3. Which FFP will you accrue the miles to?

A RTW ticket (OneWorldExplorer) might be a good solution, but you need to be away for at least 10 days (from BRU), and ready to take the "other" way home - TPAC (TransPacific) + TATL (Transatlantic), consuming at least one day extra, but enabling you a stay in one or more North American destinations.

Examples:

Travelling in C or Y: BRU-HEL-NRT (AY) NRT-PVG (JL) PVG-HKG (KY) HKG-JFK (CX) JFK-BGI (AA) BGI-MIA-ORD-BRU (AA). This is still only using 9 of 16 possible segments, but accruing MUCH more miles, to use for future travel. Look at the stickies starting the OneWorld forum and get inspired!