Question

How many semicolons can you use in a row?

Answer 1

One or several but not more than you need.

Explanation:

Semicolons should be used to link a series of phrases or sentences closely.
Examples:
He saw a beautiful deer in the wood; he stalked it carefully; he destroyed its magnificence with a blast of his shotgun.
He looked up at Cathkin Peak: a mighty block of wrinkled stone; an awe-inspiring tribute to nature; a stiff challenge for the mountaineer.