Them requiring you to sign a retainer is different. Paragraph 4 could be a problem.
If your claim is successful, then you agree to pay to the attorneys a fee equal to 40% of the gross amount recovered for you.
Under no circumstances will the attorneys collect an unreasonably large fee.
Under no circumstances will you ever owe attorneys’ fees beyond a portion of your recovery.
If your claim is successful, you agree to reimburse the attorneys from the remainder of the recovery for the expenses the attorneys advance on your behalf to pursue your claim. These expenses only include things reasonably necessary to pursue your claims, such as filing fees, postage, arbitration costs, court reporters, transcript fees, payments to expert witnesses and consultants, travel expenses, and all other litigation and arbitration expenses that we in our professional judgment determine to be reasonably necessary in connection with prosecuting or settling your claim. If we represent more than one client with claims similar to yours (which we intend to do), we may apportion expenses that go toward pursuing the claims of all clients on a pro rata basis among you and similar clients, but only if those expenses can reasonably be viewed as benefitting you and the other clients. Also, the law may, under certain circumstances, allow us to petition the court or an arbitrator for an award of attorneys’ fees that the Company (not you) would have to pay. You agree that the attorneys may petition for that award and that any such award will belong to the attorneys. You grant the attorneys a lien to secure payment of the fees and expenses described by this agreement.
The 40% is not unreasonable, but making me agree to expenses beyond the 40% fee is getting a bit greedy, and could be shady.