I'd like to strike up a relationship with a lender such that I'd be "pre-approved" up to an agreed upon limit (perhaps, something like $200,000 to get started).  

someone once asked him  if striking out upset him. he said " no, because it puts me one step closer to the next home run". forget the nay sayers. i started out with $2000 and a dream. i own and  have owned several houses along the way. i have more than $2000 now and still own the first house i bought. you just have to get out there and do it. learn along along the way, do what you can and learn what you don't know. just do it. 

@Randy Philpot Not to pile on, but this strikes a nerve with me.

However, if you can save that much extra per month, you will have plenty if disaster strikes. 

Strike a chord with them and make it personal.

I don't know if one of my properties will get damaged by a drunk driver or burned down by a lightning strike so I have insurance to cover that risk.

The latter implies always looking and being ready to strike when you find a deal. 

@Chris WilliamsYour thought process sounds strikingly similar to mine.

Talk to anyone around you when you're standing in line at the store, having a meal out somewhere, ... just strike up a chat.Ask folks what they do - they'll likely ask you the same.

You wouldn't have to wait until the end of the 4 - 5 year investment period before striking out on your own if that is what you want to do, just until you're comfortable you've learned what what.Before or when making the jump to multifamily, to greatly increase your odds for success you could hire a multifamily mentor or coach.