The error that you received indicates that you have very few unspent transaction outputs (UTXO's, or "unspents") in your wallet. When you have very few unspents in your wallet, it becomes extremely difficult to make multiple transactions from the wallet.
We have a feature in the API that allows you to create additional unspents in your wallet, called "fanout". You can use this to divide one of your unspents in your wallet into multiple smaller unspents, which will allow you to use those multiple unspents to send multiple transactions.
Information on this function can be found here for V1 of the API: https://bitgo.github.io/bitgo-docs/#fan-out-unspents
For V2 of the API, refer to the following: https://www.bitgo.com/api/v2/#fanout-wallet-unspents