Multi-dimensional range queries play a crucial role in various collaborative data analysis tasks, such as healthcare insurance, retail customer observation, and financial risk management. These queries across different platforms enable users to obtain precise and comprehensive research data, which cannot be achieved with single-table queries. To protect privacy, many researchers have focused on designing privacy-preserving range query schemes. However, when these methods are applied to multiple tables, existing solutions face security and efficiency issues. The security concern involves the exposure of intermediate results in each table, which can reveal whether the information of a research object meets the query range of each table. The efficiency problem arises from building an index on large-scale data for each table and the requirement to scan each table thoroughly. To address these problems, this paper proposes a privacy-preserving collaborative multi-dimensional range query scheme that balances efficiency and security in multiple sources scenarios. We first introduce a secure construction scheme for a collaborative R-tree among multiple sources. Additionally, we propose a pruning strategy based on dimension sensitivity to accelerate secure multi-dimensional range queries. Theoretical analysis and experimental results demonstrate the security and effectiveness of our method.