The phrase 'come up with a design' is correct and usable in written English. You can use this phrase when you need someone to create a design for something, such as a new logo for a company. For example, "We need to rebrand our company, so please come up with a design for a new logo that will better represent our values."
We figured the magazine should have a web site so we asked our Quark designer to come up with a design.
Instead, consider partnering with a designer who can help you to come up with a design for that will represent your brand across all of its digital channels including its social media, advertising, and offline marketing efforts.
We will expect you to come up with a design that makes sense.
It took him a week to come up with a design.
Beller had only a week to come up with a design.
The architects have to come up with a design and then you have to get it approved.
One of the students, Varunan Kumar, had come up with a design involving a spiral wrapping around itself in space.
And Sam and other youth have come up with a design for a Moringa grinder, which is currently being constructed.
After receiving the curtain commission in September 2008, Mr. Kuitca struggled to come up with a design.
Earlier this year he was asked to come up with a design to celebrate Lacoste's 80th birthday.
1. Come up with a design that you can easily cut out of the paper with a craft knife.
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