The House of Lords voted in favour of five amendments over two days of debate, leading the new government to its first parliamentary defeats.
The changes included backing the Dubs amendment to protect the rights of refugee children after Brexit.
No 10 said they were "disappointed" by the move, but planned to overturn them when the bill returned to the Commons.
If the amendments are voted down by MPs on Wednesday - highly likely due to the Conservatives' 80-strong majority in the House - the so-called "ping-pong" period between the two chambers will begin.
This means the bill will pass between the two Houses until both sides agree on the wording.
The Brexit bill - officially called the EU (Withdrawal Agreement) Bill - ensures the UK leaves the EU on 31 January with a deal.
It passed through the Commons unamended by 99 votes, but has had a tougher battle through the Lords.
On Monday, peers agreed amendments on EU citizens, EU Court of Justice rulings and court independence, seeing three defeats for the government.
Earlier, the Dubs amendment - allowing child refugees to be reunited with their families in the UK post-Brexit - passed by 300 votes to 220, making a fourth loss.
A short time later, a fifth amendment narrowly got the backing of peers - with the government losing by 239 votes to 235 - changing the bill so it makes note of the Sewel Convention, under which Parliament should not legislate on devolved issues without the consent of the devolved institutions.
The amended bill was passed by peers on Tuesday night without needing a vote, and will now return to the Commons on Wednesday afternoon after Prime Minister's Questions.
Did you hear that we're writing Iraq's new Constitution?
Why not just give them ours? We're not using it anymore.