Can I compute convolution through the overlap and add method without the IFFT? So, I'm (I think) aware of how the overlap and add algorithm for linear convolution works, but my question is that, suppose I have a FFT-ed set of sequences that belong to a large sequence.


Can I add the overlapping parts before taking the IFFT of each sequence?
Can I add the overlapping parts and then perform another convolution without taking another set of IFFTs and FFTs?
Let's say that I have a function which multiplies by 3 if the number is 0 in the time domain, but multiplies by 6 if it isn't. I can perform this with only one IFFT as opposed to an IFFT+ a FFT by taking the IFFT and then multiplying in the frequency domain by the required number. Can I do a convolution through overlap and add, apply the aforementioned function through the "one IFFT only technique" and then do another convolution through the overlap and add method without having to do another set of FFTs for the next convolution through the overlap and add?
your FIR, $h[n]$ can be converted, once and for all, into $H[k]$ the spectrum with which you will multiply in the frequency domain.  but for every frame of $x[n]$, you must zero pad and FFT that into $X[k]$, multiply that $X[k]$ by $H[k]$ (which now becomes $Y[k]$) and you must iFFT that back into $y[n]$ and overlap add with the previous frame of $y[n]$.