可以。According to the relevant provisions: the enterprise has registered with the customs declaration unit (that is, has registered as an "import and export consignee" or "customs declaration enterprise"), can directly apply to the customs to increase the cross-border e-commerce qualification。There is no need to apply for registration of information without declaration rights。
Details of specific laws and regulations can be found in the following announcements:
(1) Notice on Regulatory Matters Relating to Cross-Border E-commerce Retail Import and Export Commodities (Announcement [2016] No. 26);
(2) Notice of the Inspection Department on Matters related to the Information Registration of Cross-border E-commerce Enterprises without Declaration Rights (Inspection Letter (2016) No. 13) (inside)。
Source: China Customs Network