I have a business trip in late May from either JFK-DPS or LAX-DPS.
This trip is on the company's tab and the price range is capped at 2200.

I am trying to do the routing my own with a week long stopover at NRT or HND.

Ultimately I would like to fly the long way from JFK (through euro) LAX is back up option, stop in NRT/HND for one week and continue on to DPS. Dates leaving May 25. Returning from DPS-LAX June 23.

I am having trouble searching ITA and finding anything worth selecting.

If anyone could shine me in the right direction that would be great.
Also would like to put all the miles into one carrier if possible.

Thankyou