My spouse had a similar situation a few years back. The company would send their employees transpac and to Europe, occasionally in business class, through a well-known corporate travel agency.
I made the company an offer: if I could send all of our family over for less, would they cover it? In other words, if I could arrange our ticketing/accommodation for less than the price they were going to pay for my spouse anyway, would they go for it? I might have mentioned in the bargain that their employee would be happier having the family along, might be agreeable to even more business trips, etc.
The company did go for it. It was a breeze to find consolidator fares for four that beat biz fares, but I could usually do it for regular coach fares too. We stuck to a lot of Holiday Inns due to their kids free policy (a bargain in Japan especially). We still managed to rake in miles for future family trips.
So everyone came out ahead, thanks to a flexible company policy.
In a sense, then, we got miles and cash. And they had a contented employee.