Parametric EQ vs multiple bandpass filters Will filtering a signal through multiple bandpass filters, where each filter is passed the complete signal, and then combining the output have the same result as a parametric EQ?

What if the signal is passed into a series of bandpass filters?

Are there any performance issues or optimizations that can be made when EQing a signal this way?

Update:

After reading the answer in this question which-filter-for-an-audio-equalizer it seems splitting the signal through a filter bank (in parallel) is the correct way.

The answer explains how the bands need to blend together to avoid audio issues, how is this calculated if each bandpass filter can have a varied bandwidth?
a graphic EQ need not mean cascaded shelves.  it could mean cascaded peak/cut bell filters.  maybe with shelves as bookends, maybe not.

the bell filters are symmetrical in log freq (or the pitch scale) and are naturally spaced equally in log frequency.  you can draw any reasonable shape with a sum dB of these cascaded peak/cut filters.  but nothing too wild.

you could also do this more analytically with a sum of FIRs, all time-aligned.  make a series of overlapping complementary window functions (like a Hann) but operating on log frequency instead of linear frequency.  but that frequency response can be interpolated and sampled in linear frequency and an FIR can be derived from that magnitude response with a delay of some sufficient constant value.