Is it possible? Yes
Is it advised? Absolutely not
Amazon API Gateway's is a multi-tenant service with shared architecture. Each API is not serviced by a single resource, but a set of shared resources that scale with overall usage. Implementing load balancing in front of a set of API Gateway APIs within the same region would be redundant and just add an additional network hop to your customers traffic.
Customers are assigned default limits to prevent abuse and for capacity planning, but these limits can be raised if you have a valid business need for them to be.