What is a Companion Score™?

Question

_{This is in the spirit of the What is a Word/Phrase™ series started by JLee with Score version puzzles.}

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If a word could be calculated score with a specific metric, I call the score as a Companion Score™.
Use the following examples below to find the metric.

$$ % (purpose-specific template, not for general use) % \def\Pad{\P{2.0}} \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\textbf{ Example Words }\Pad}\def\NT{\textbf{ Companion Score}^{\;™}\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{Conifers modified 2019.9.9}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ OBJECTIVE }&\text{ 0 }\\ \hline \text{ WHENEVER }&\text{ 0 }\\ \hline \text{ COUNTEREXAMPLE }&\text{ 0 }\\ \hline \text{ OXYGEN }&\text{ 1 }\\ \hline \text{ PERFECTION }&\text{ 2 }\\ \hline \text{ HIJACK }&\text{ 2 }\\ \hline \text{ ZOOKEEPER }&\text{ 2 }\\ \hline \text{ STUDENT }&\text{ 3 }\\ \hline \text{ BATTLEFIELD }&\text{ 3 }\\ \hline \text{ POSTPONE }&\text{ 4 }\\ \hline \end{array}$$

And, if you want to analyze, here is a CSV version:

Example Words,Companion Score™
OBJECTIVE,0
WHENEVER,0
COUNTEREXAMPLE,0
OXYGEN,1
PERFECTION,2
HIJACK,2
ZOOKEEPER,2
STUDENT,3
BATTLEFIELD,3
POSTPONE,4

Open Bonus Question:

What word you could find with the highest Companion Score™ ?

Answer 1

A Companion Score is

The number of pairs of adjacent letters in the word which are either the same or adjacent in the alphabet.

Examples

PERFECTION has 'FE' and 'ON', so scores 2.
ZOOKEEPER has 'OO' and 'EE', so scores 2
STUDENT has 'ST', 'TU' and 'DE', so scores 3.

Bonus question

The largest Companion Score I have attained is 7 with the following examples:
FIDDLEDEEDEE, NONCONSTITUTIONAL and NONOPPOSITION