I'm trying to use some capacitors I have on hand for filtering power supply, I want to use the following with the 100uf/350v in series ...
I
think your question was, "Can I use 2x 47uF and 1x 22uF caps, rather than the stock 3x 20uF caps?" Is that correct?
The answer is yes, you can.
... I read about doing cap job and using different values, since some of the values aren't available and that it can "tighten up the bass". If I can use these values, how will it effect the sound?
How will it sound? I dunno, it sometimes varies by specific amp-topology. Personally, I'd just try it an see what you think.
The amp will only "tighten up" if the amp circuit in question typically draws a lot of current, and was under-filtered to start with. That is, Small Filter Caps + Big Pulses of Current Draw (mainly from output tubes, with big signal) = Supply Voltage Sag.
Small filter caps store less charge, which is drained away more-easily by heavy current demands, resulting in the voltage at those caps dropping. But that supply voltage sag also is affected by the rectifier & power transformer's ability to re-charge the filter caps. Low-resistance rectifiers (bigger tube or solid-state) and low-resistance power transformers (big core and big-wire windings) enable faster re-charge of filter caps. Drain and recharge happen for different lengths of time, with the drain portion typically being much longer than recharge. And how low the voltage dips during drain is all about filter cap size and circuit current demands.
This is the long way to explain that bigger
preamp filter caps (which is what I think you're asking about) probably won't translate to the solid-bass effect you've read about, because preamp stage current demand is quite small. I'd expect an audible sound/feel change to occur when raising filter cap values for the output tubes (plate and possibly screen), because that part of the circuit draws very much more current from the power supply and is more likely to exhibit voltage sag with small filter caps.
As Eleventeen notes, a too-big filter cap right after the rectifier, in the absence of significant PT winding resistance or added series resistance, can draw a big enough peak current during cap recharge to pop a rectifier.