I take a pragmatic view regarding people who say they can do it all: either they are lying or they have never been involved in an intense firefighting situation. Either way, you don't want to work with them.

Figure out what skills are needed and get them. This is not always so simple, because sometimes the skills are diverse and not available in your group (and perhaps, they should not be available in your group). For example, the typical DBA group will not have operating system tuning experts and application functional experts. The key is clearly identifying the required skills, regardless of where the skills reside. First deal with the scoping, or the definition, and then work to secure those skills.

Most firefighting situations require a very diverse set of skills. For example, you may need Oracle diagnostic, SQL tuning, and operating system tuning skills. But I'm willing to bet you also need someone who is an expert on how to use the application. If your users are new to the application, it's a good bet they are trying to use the new application in the same way as they used the old application. While they may get the work done, it might not be the best way to use the new application's capabilities. This directly impacts the system, because the users may be requiring the system to do more work than necessary. The problem is that you and your management team won't know this, but a functional expert will. So consider investing in someone who can help your users. The reduction in system workload can have a dramatic impact on performance.