Yes and no. It depends on what you mean.
In Bitcoin you can have multiple inputs and multiple inputs so you can combine tx fees. In Ethereum, a transaction is from one address to another address. If the "to" is a smart contract, then it could potentially do something with the transaction and send call functions/send ETH to multiple addresses (a "transaction" from inside a contract is called an "internal transaction", but that's a misnomer because it's not a real transaction).
Since smart contracts on Ethereum on turing complete, you can group contracts together if you want, you just can't full group tx fees. However, if smart contract A had a requirement like a 20 ETH minimum deposit, you could write another smart contract B that took multiple transactions and as soon as the total hit 20 ETH, it would send it to contract A. This allows people to "group" transactions in a way.