The count URL parameter can be added to the end of the API URL to increase the page size by as many as 999 records. If you input a value higher than 999, the count automatically reverts back to the default count of 100.
If there are more than 999 records, you'll need to fetch the results page-by-page and then combine them. The HTTP response from the API includes a header called X-Total-Count which has the total number of records available for a particular request. Dividing this number by the page size (rounding up) tells you how many pages of data there are. You can then use the page URL parameter to fetch pages beyond the first.