gain ****
advance ***
win *****
pull ahead
make headway
get ahead
gain ground

But they didn't stay long enough to make any headway, he said.

But he wasn't making any headway with the big man.

Or with almost anyone else who is trying to make headway through another day in life.

But administration officials are also trying to make headway on their own.

They'd make better headway now, could see where they were going.

We are making very good headway in research and development.

Next, we must try to make headway in the political field.

But he was out of action long enough for me to make some headway against his men.

The Government has made some headway in both, but not much.

Because you couldn't make any better headway against the east wind than I did?