According to the book 'Influencing: Skills and techniques for business success' by Fiona Dent and Mike Brent, there are two major influencing styles. Push tends to be directive. It tells, and is clear and resolute, but needs to be employed in situations where firmness is required because of difficulties that exist or weakness is evident. Pull is more participatory and collaborative. It seeks to incorporate everyone's perspective. It can appear wishy-washy if not skilfully employed. Thatapproach should be followed which is most likely to secure commitment and not mere compliance.
The two divisions can be further divided into four style categories: directive; persuasive reasoning; collaborative - team oriented, people oriented to inspire them with a vision. The directive style relies on your expertise and reputation being respected by others, and where there really does seem to be one answer. It is
"I" driven whereas persuasive reasoning is more "we" and issue driven. Directive styles can make the user appear as "a bull in a china shop"; persuasive reasoning can be portrayed as tough guy.
Collaborative influencing takes the "we" element further and seeks to mobilise everyone's ideas in a journey of discovery. It may have the flavour of "I'm your best friend", which may not go down too well. Visioning style is concerned to stir people's emotions in support of achieving an objective. This last one has been used by demagogues to stir people's hearts and minds for evil purposes as well as good.
A useful table offers the benefits, problems, words and body language associated with each style along with advice on when to use and when to avoid each. Cases and exercises illustrate these styles.
Empathy comes in for extended treatment with the definition of "standing in the other's shoes". This does not necessarily happen just intuitively, and therefore before a specific influencing effort there should be an intense effort to think about the other person or persons and to sense what it might feel like to be them - their hopes, fears, concerns, what turns them on, what turns them off, where are they coming from.
Reference:
Influencing by Fiona Elsa Dent and Mike Brent, 2006 (bd-cons.com)
CIPS study guide page 163-165

For low-value, routine purchases, the involvement of The procurement manager (C) and An internal business user (E) is appropriate. The procurement manager brings expertise in supplier engagement, while the internal business user provides insights on specific needs for the product or service. Involving high-level roles, like the CEO or a legal advisor, is unnecessary for routine purchases, as per CIPS guidance on resource alignment in procurement.

Reference: CIPS L4M5 Study Guide, Section 2.3 - Market Factors and Analysis

Trust-building behaviours are as following:
Joint-effort issue resolution
Open sharing of information
Open and honest discussion on root cause of failures
Joint planning focusing on value for money and risk sharing
Commercial transparency and co-proposition of cost reduction and service improvement programmes Joint recognition and celebration of successes

Hypothetical ("What if...") questions test possibilities and invite creative options without binding either side.
They help probe interests and packages while keeping commitment provisional.
Reference: CIPS L4M5 (2nd ed.), LO 3.2 - Questioning styles (open, probing, hypothetical) in persuasive negotiation.