How did the number of slaves increase in Rome?

Ancient Rome was an extremely aggressive militaristic state that conquered all of Western Europe, the Mediterranean, and North Africa. And the main source of slaves was the circulation of the population of the conquered territories (the bulk of them were Germanic tribes – Alemanni, Gaul, Swabian).
However, they could turn into slavery for debts, the head of the Roman family (pater familiae) had the right to sell his family members (for example, children) into slavery. Children of slaves also became slaves.