If a loan is current reported on the credit file (while it will be given it was approved weeks ago) monzo will, or used to, take that into consideration even though it was their loan, and meant claimants were not able to apply for another right away.
Your best bet is likely to find another loan with someone else, depending on how recently you borrowed the money, it may not be on your credit report yet so you might find approvals easily. If it’s already on the report, it may be harder but still should be possible if your credit rating is okay.
If you repay your Monzo loan, that might take up to six weeks to show on your credit file as paid back, during which time it might be harder to borrow. Additionally, some lenders might not like that you’ve paid something back early, so that could make it harder and it’s a lottery as to whether Monzo will offer you a new bigger loan or not.
Really, it’s all guesswork but it’s worth a search now, usually the loans linked through one of the credit rating products like ClearScore or Credit Karma are a good place to start as you might find you are pre-approved through them for one.