The phrase "build up something" is correct and can be used in written English.
You can use it to refer to the process of constructing something or increasing something in size or intensity. For example, "We need to build up our savings if we want to achieve our financial goals."
You build up something on the balance sheet, and you pretend you are getting rich".
"It is important to build up something more positive but with a certain gravitas".
We should try to build up something on legal grounds so as not to play into the hands of the authorities".
This is one of the good memories and I think we can build up something strong for the next few years.
The same way that people love to discover and play with new Google Doodles or Snapchat filters, Messenger could build up something similar that is engaging in new ways.
They see investment in a game as a long-term thing, a way to build up something that will last 10 or 20 years and make billions in the process.
The couple have built up something of an impressive record of brushes with the law.
She certainly could have gone anywhere, but it's wonderful that she could have built up something like this at a place like the College of New Jersey".
One legacy of the World Cup has been a heightened appreciation in Brazil of all things German, particularly Lukas Podolski, who may not have played a central role in the tournament but has built up something of a cult following with his unfailingly genial comments about Brazil on Twitter.
I thought he knew that in "Newt, Inc". he had built up something good in his years out of public office, and that he wouldn't risk damaging his operation by running a race that made him look like he wasn't a powerful figure in the Republican Party.
I wanted to do something that started from ground zero and a blank canvas, and built up something new again.
