Please input: if fly LAX-FRA stay there few days-FRA to MAD-stay there few days-MAD-LAX. Would you for trip in early February:

1-Choose 40,000 Miles used on AA Award flight?
OR:
2- Try to get pay multi stop ticket to get more new miles? One consideration is that by introducing the MAD stopover the pay ticket costs go up substantially--2 to 3x the FRA or MAD only pay ticket.

I'd go on the value of the miles vs. the value of the ticket plus miles earned... let's say for simplifying the math that the multistop ticket earned 16k miles.

Let's also call the miles worth 1c each, which of course is quite subjective(*) ... so the "free" ticket is worth about $400 + taxes... meanwhile the rt lax-fra-mad-lax ticket costs $n - $(miles divided my 100). Odds are, if it's a 2-3x factor, it's a lot cheaper to use the award and as such it's a good use of the award (barring any making status issues.)

(* I personally find that a bit low for EQM, for example - would you be risking status for the year by not going on a paid ticket?)

Now, on a separate note, have you tried pricing it as one of the following:
- AA LAX to FRA, separate FRA<->MAD round trip
- AA LAX to other european hub (LHR or BRU), separate ticket hub to FRA to MAD to hub (or even as two hub<->FRA/hub<->MAD tickets)
These are often enough, in my experience, cheaper - although it may take extra time since you need to leave slop since they're in two itineraries.

Have you priced an open jaw LAX-FRA and MAD-LAX? One-way FRA-MAD is around $100 on Condor or Air Berlin.

Neat suggestions. Will look into them.

Open jaw is good alternative.