The following are just "suggestions". I am just suggesting, I am not trying to "made" you do as I told. So please don't get all mad etc. (I have to explain this, coz some people think irrationally and think I am "telling" them to do it this a that way.)
I think of 5 options.
Option A B: However, they are not Greek Goddess style. Option C D E: it's greeklike
Please please please "try/test" first before you do it "permanent". Coz I don't know if it's gonna work or not.
Option A (regular style dress)
Add elastic inside (between the green dots)
And the dress may be a bit plain with just that elastic, so you can add a sliver belt etc, but it's up to you.
Option B ("Carmen")
See the "T" (the white line), that's a transparent bra strap.
Pink:the elastic strap (lace-like) attach to the dress
Red:the drapery sew around the opening.
Color red/pink? it can be whatever color, I choose those color just to explain to you more easily.
If the work place still not allow that style, well, then add a scarf, like how people wear their scarf when they go to ball dinner. Option C GREEK
Not sure how your armpit area of the fabric is. The wwww part of the chest area fabric, you can turn into a elastic wrap around you, and it can create some fold and thus greek like too.
Again, you can use transparent bra strap.
Blue: soft fabric that look like a scarf, or if you have a long scarf and it matches, why not. (can be any color, such as white)
And for the end of the dress, may be cutting it diagonally would make it look more greek too. It'll be nice to match with a ballet style shoes and then some gold strings on the feet up to the knee. etc.
Option D GREEK
I know I know, the statue is a guy. But you are a lady, it's OKAY.
I like the 'scarf like fabric' that lay on his shoulder. It's a similar affect with Option C (the blue color). (hope you know what I mean)
And yeah, add some leaves wreath on your hair, that would increase the greek look.
Option E GREEK
No, I don't mean the to "low" V cut as low at her dress (that may not appropriate to wear to work)
I mean, can you kind of cut the dress a bit and turn it into the "y"
Hope things will work out and have fun. Take it easy coz you are doing all this because you want to have fun, so don't stress out yourself.