This question requires identifying the specific regional grouping among the given options where India does not hold full membership. Let's examine India's association with each mentioned group:

Understanding BASIC

BASIC is a bloc comprising four major emerging economies: Brazil, South Africa, India, and China. India is a founding and full member of the BASIC group, established to coordinate positions on climate change issues.

India's Role in G-4

The G-4 group consists of Brazil, Germany, India, and Japan. These nations support each other's bids for permanent seats on the United Nations Security Council. India is an active member of the G-4, working towards UN Security Council reform.

Exploring BRICS

BRICS is an acronym for Brazil, Russia, India, China, and South Africa. It represents major emerging economies that collaborate on various global issues. India is a foundational and full member of BRICS.

Shanghai Co-operation Organisation Membership

The Shanghai Co-operation Organisation (SCO) is a Eurasian political, economic, and security alliance. India officially became a full member of the SCO on June 9, 2017. Prior to this, India was an observer member starting from 2005. The question asks to identify a group where India is *not* a full member. Based on the timeline of India's full membership, the SCO aligns with this condition, particularly if considering periods before its formal accession.

Therefore, among the options provided, the Shanghai Co-operation Organisation is the regional grouping identified in the context of the question where India's full membership was acquired later compared to its foundational role in BASIC, G-4, and BRICS.