The in-tank pump, or transfer pump, can cause driveability problems and lack of power when it is bad. It can be difficult to troubleshoot because the car will still run even when the pump is completely dead. If you have determined the the transfer pump is dead, the classic Chevy Vega pump trick works well. Chris Guy has the Vega pump info at his E28 site. I bought a Vega pump from a local parts store for about $25 and installed it in less than an hour. I encountered two problems doing this. First, I had no idea what year Vega pump to ask for. I told the guy behind the counter I wanted to put it into my BMW. He laughed and then picked some random year for me. When I got home, I pulled the transfer pump and foud that I had the plastic body pump with integral mount instead of the metal pump with bolt on mount (problem #2). Supposedly, the metal version is a direct swap with the Vega pump. Since I did not have the separate mount, I just used a couple appropriately sized hose clamps to hold the Vega pump in place. The car ran better the first time I started it up.
The main fuel pump is overly taxed when forced to run without the transfer pump in operation. Since My car ran with a bad transfer pump for an unknown number of miles and my car has 238k miles on it, its probably time to replace it. Better now than when it strands me at the track. Since my car will soon have significantly more power than stock (~50% more) and even more next year, I figured more pump is better than less. Although BMW uses very good fuel pumps from Bosch which are more than capable of the power levels my car will soon see, I don't want to change fuel pumps twice. The pump I found is commonly used on 600+hp supercharged Mustangs and Camaros/Firebirds. It is known for being able to run non-stop for months at elevated pressures (75+psi) without failure so it will last a long time at 3 Bar (43.5psi) in my car. It wasn't cheap at $200 but a replacement Bosch stock pump is even more. I'll give details when I finally get it in. I tried fitment i the stock pump mount and found it is slightly smaller in diameter that stock so I will have to shim it somehow to prevent it from dropping out at the wrong moment. I am also unsure about the power requirement. I hope to use the stock wiring and fuse. If I can't, at least the pump came with a very nice wiring harness and inline fuse block assembly.