I have got a plan to find him

=I have planned to find him

解析：不定式to find him作后置定语修饰前面名词a plan，不定式与被修饰名词属于同位语关系。可以用这个名词的动词形式后面接不定式作宾语，即I have planned to find him.

make/get a plan to do sth类似于make a choice to do sth都可以改为动词后接不定式作宾语

(1)make a plan to do sth=plan to do sth

(2)make a choice to do sth=choose to do sth

(3)make a decision to do sth=decide to do sth

备注：不定式作定语与被修饰名词存在有以下几种关系

(1)动宾关系

He has much work to do.

(2)主谓关系

She is the first person to come here

(3)动状关系

Spring is the best time to plant trees

(4)同位关系

He made a plan to learn English