Yes, you can hold several American Express Business Cards at the same time.
This is especially recommended for frequent travellers who want to take advantage of the benefits offered by each of these cards (access to airport lounges with the Business Platinum Card from American Express, benefits with Air Canada with the Aeroplan* Prestige Card from American Express, annual one-night free certificate at Marriott Bonvoy hotels with the Marriott Bonvoy Business Card from American Express*).