Z Capital Group plans to raise at least $1 billion for a fund to prop up smaller companies and businesses in need of cash, as political uncertainty threatens to roil markets and puts new targets up for grabs.

The firm, known for its investment in the Mrs Fields cookie brand, could round up as much as $1.25 billion for Z Capital Partners III, according to a November letter to investors reviewed by WSJ Pro Private Equity. Z Capital expects the pool to surpass the $750 million private equity fund the firm raised in 2014.