I haven't found a retail broker that accepts orders in fractions of a cent. One of the scandals that was reveal in Michael Lewis book Flash Boys is that exchanges gave high frequency traders a variety of order types (beyond basics, like limit, market, all or none, fill or kill....) and the unique ability to make fractional penny bids and asks.
I had not tried it before so I just gave it a shot.
Schwab
The Limit price you have entered is invalid. Please change this order and enter a valid price.
This stock is trading in decimals with a minimum price increment of 1 cent.
TD Ameritrade (with thinkorswim)
REJECTED: Orders above $1 can be entered in no more than 2 decimals; orders below $1 can be entered in no more than 4 decimals.
So, AMTD allows it but for penny stocks. I won't be taking advantage of that feature. :-)
Thinkorswim does have many different order types: market, market on close, limit, stop, stop limit, trailing stops;
with different time in force: day, am, pm, extended, good till cancel, good till cancel including extended;
with different instructions: all or none, fill or kill, none;
with different exchange routing: best, arca, nasdaq
That's just the specs for a single order. You can also program sequential orders in very complex ways - a simple example is to have a buy order with a limit price and once that executes it sets up a sell order with a trailing stop.
I've used market, limit, stop, trailing stop with day, gtc. I've never used AON or FOK and always route to the best exchange. The only thing I've considered for sequential orders is the simple example I gave.