Line a 16-cup (10-inch) Bundt pan with plastic wrap, leaving about a 2-inch overhang on all sides (it's okay if the plastic wrap doesn't go completely up the sides of the center column).
Combine the cream cheese and sugar in a large bowl and beat with an electric mixer on medium-high speed until smooth, about 3 minutes; scrape down the sides of the bowl as needed. Add the cream and continue to beat, starting on medium speed and gradually increasing to medium high as the mixture thickens and finally forms stiff peaks, about 4 minutes.
Evenly spread about 1 1/2 cups of the whipped cream mixture on the bottom of the bundt pan. Top with 16 overlapping cookies to cover. Evenly spread about a third of the remaining cream mixture over the cookies and top with a layer of 16 overlapping cookies on the outer ring of the pan and then 6 halved cookies (snap them in half with your hands) on the inner ring of the pan to cover. Evenly spread out half of the remaining cream mixture and top with a layer of 16 slightly overlapping cookies on the outer ring and about 8 slightly overlapping cookies on the inner ring of the pan to cover. Finish with the remaining cream mixture and spread evenly, then loosely wrap the cake with the plastic wrap overhang. Refrigerate 12 hours and up to overnight.
Put the remaining cookies in a resealable plastic bag and crush them to crumbs with a rolling pin or the bottom of a measuring cup; reserve.
When ready to serve, unwrap the plastic wrap and invert the bundt pan onto a serving platter; remove the pan and carefully pull off the plastic wrap. Using your hands, press the gingersnap crumbs against the bottom of the cake about one-third of the way up the side. Drizzle the top with the caramel and chocolate sauces. Cut into slices with a serrated knife.