Sandwich Shop in DC/Arlington/Alexandria
I used to live in Miami and there was small chain market there called Gardner's Market. They had lots of nice quality, overpriced groceries but the real draw was the deli. You could pretty much take anything in the store back to the counter and they'd throw it in a sandwich and charge you like $8. Basically there were limitless possibilities and I was once made fun of by the lady making my sandwich for not getting more fillings.
I've spent many a weekend trying to find someplace similar in the area to no avail. Along the way, I've certainly found a lot of decent sandwiches so what I'm really after at this point is somewhere with quality meat, cheese, and fillings and either a TON of selection or somewhere that will allow extreme customization.
There is a bakery in Shirlington Arlington called Best Buns. They have great deli type sandwiches and other great bakery goods! I am not sure on the customization, but the bakery chef there is very nice.
In DC I like So's Your Mom for great sandwiches with lots of options. And apart from the wide selection of sandwiches they offer, you can more or less custom make any sandwich.
It's in Adams Morgan. Cash only.
Phillip's Cafe doesn't have a huge selection, but they make some great sandwiches. The hand carve roast beef, ham and turkey and pile it high on the bread of your choice, with a nice variety of toppings. It's not cheap (around $8 a snadwich, cash onnly), but it's worth it.
I think they have two DC locations. I go to the one near Mass Ave. and N. Capitol St. a couple of times a week for lunch (and coffee in the morning).
They don't have everything put into a sandwich, but Earl's Sandwiches in Clarendon is quite good and I am sure they would let you customize. The Italian Store is also great sandwiches and you can customize. Also I know Whole Foods in Annapolis used to have a great sandwich making place, I don't know if the one in Arlington does too?
Lost Dog Cafe in Arlington on Washington Blvd, west of Ballston.
Over 50 sandwiches available. My favorite is the big dog. Sooooooo good!
Their sister restaurant, Stray Cat, is in the same shopping center. I don't believe they offer carry out like Lost Dog, but if you are there to sit down and eat, they never have a line like Lost Dog does. They carry about 1/3-1/5 of Lost Dog's sandwiches. Lost Dog actually has a deli counter, with a restaurant on one side. Stray Cat is all restaurant.
Not exactly what you are looking for, but a ton of selections and I believe you can build your own. They have good pizza too.