If you have run into an error when trying to upload images to a site within a WordPress multisite network, there a couple of settings that you can check to see adjust the limits.
Max upload file size
If you receive the error "FILENAME exceeds the maximum upload size for this site." this indicated that the individual file has exceeded the limit set in WordPress Network Dashboard => My Sites => Network Admin => Settings
Navigate to this admin options page and look for the setting Max upload file size (by default set to 1500 KB)
Upload Limit Exceeded
If you receive the error "Sorry, you have used your space allocation of (x)MB. Please delete some files to upload more files." then your individual sub-site has reached the maximum combined limit of files allow to be uploaded.
As a network admin, to fix this navigate to the same settings page WordPress Network Dashboard => My Sites => Network Admin => Settings and look for the Site upload space limit.
Be aware that these settings will affect all websites in the network.
