If I am eligible to contribute to several IRS-recognized tax advantaged accounts that have separate limits (HSA, 401K, 457, IRA, etc) can I fund the contributions with prior savings when my gross income is less than the combined contributions, but greater than each individual account yearly limits?
Well, many of the tax-advantaged plans that you are planning on investing in are funded via payroll deductions and not by cash contributions, and so you are certainly limited in all these contributions by the individual gross incomes from each payroll activity; your employer is not going to send more money to your 401(k) as an employee contribution than what the employer is paying you. With the IRA contribution which must be paid in cash to the IRA custodian, you are limited to $5500 or your total compensation (earnings such as wages), whichever is less, and so you could contribute your entire compensation (taking money from your savings to cover the SS and Medicare tax, Federal and State income tax etc deducted from your wages before you got your hands on the rest a.k.a. your take-home pay), but then, what are you going to live on? That being said, I know of several teenagers who contributed their entire compensation of $5500 or less from mowing lawns etc to their IRAs with their parents gifting them the money to cover the shortfall due to tax withholding, and of course, providing support for daily needs.