"greater quantities of" is correct and usable in written English.
You can use it when you want to indicate that the amount of something is more than in the past or than is typical. For example: "Due to the increasing demand, stores have been forced to purchase greater quantities of stock."
China's need for ever greater quantities of imported oil is driven by its torrid economic growth.
It pays them enormous sums, and invests far greater quantities of money in their promotion and their maintenance.
Meanwhile, there is no evidence that manufacturers are using greater quantities of the real, natural ingredients consumers want.
Countries with significant primary industries, such as mining or forestry, tend to emit far greater quantities of greenhouse gases.
As a general rule, the deeper deposits have higher internal pressures and contain greater quantities of gaseous hydrocarbons.
But countries with significant primary industries, such as mining or forestry, tend to emit far greater quantities of greenhouse gases.
The rivers that flow into the Tyrrhenian Sea are longer and more complex and carry greater quantities of water.
For urban communities, this will have significant benefits: greater quantities of quality water means that surrounding communities – mostly subsistence farmers – will have better crop growth and yields.
Rowling's launch of Pottermore online is set only to increase fan participation and produce even greater quantities of fanfic, including slash.
But many of these outlets have, over the years, come to serve as fencing operations for greater quantities of illegal ivory.
In west Africa, cocoa is grown primarily for export, and as the world gorges on ever greater quantities of chocolate, the demand for cheap cocoa has risen exponentially.
