Hello
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Thing is I don't want to overload the TC Electronic BAM 200 watt amp I'm using.
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The power handling of the speaker does NOT add any power to your amp and cannot overload your amp. Power handling of a cab just tells you how much power the speaker cab can handle. The speaker cab doesn't generate any power. It is passive. An amp with too much power for the speaker can overload and blow the speaker. A speaker can't overpower an amp.
One thing you do have to be careful of though is the ohms load on your amp. Typically, with solid state amps, as the ohms load goes down, the amp will produce more power. Most amps will push as much as twice the power into a 4Ω load that they will into an 8Ω load. Two 8Ω cabs running in parallel (industry standard connection) will generate a 4Ω load. That's fine as long as the amp has a minimum ohms load rating of 4Ω. HOWEVER, if you add another 8Ω cab, that drops the ohms load to 2.67Ω and if you add two of them it drops the ohms load to 2Ω.
The amp will try to put out more power into that lower impedance (ohms load) but it will overheat doing so and if the protection circuits of the amp don't kick in to shut the amp down in time, you can melt interior parts. That may well turn your nice amp into an expensive paper weight. So you need to be cognizant of the ohms load you are putting on your amp and the minimum load it can handle. That minimum ohms load rating should be printed on the back of your amp...don't go any lower than that.
When you talk about speakers separately, bear in mind that the cabinet you put them into may very well lower their power handling capability. Modern speakers are matched to the interior space of the cabinet and the type and size of ports used in it.
@Wasnex can give you some more specifics on that Suffice it to say that the speaker has to be matched correctly to the cab it's used in to both sound good and have the power handling the speaker is rated for.
Also, just about any speaker will blow with significantly less power than it's rated for if you boost the heck out of your bass EQ. It will cause the speaker to try to replicate frequencies at a high boost that are almost sub-sonic or in some cases completely sub sonic. That boost of the bass EQ requires the speaker to move exponentially further than it would without a full boost on the bass EQ and will often push the speaker past its excursion limit. At the very least it will crease the cone of the speaker, which ruins it, or physically tear the cone.
That's one of the reasons folks around here recommend High Pass Filter (HPF). That HPF sounds a little backwards at first glance, but what it does is allow any signal higher than you have it set to pass through unimpeded. If your amp doesn't have one built in, you can actually buy them as stompboxes that are adjustable. Then, if you set it at 60Hz or 40Hz, it basically rolls off any frequencies below where you set it very quickly so you don't run into those over-excursion problems.
@agedhorse actually designed some of his Mesa Subway amps to have adjustable ones that you control with a knob on the front of the amp. Playing around with that HPF can help you find the perfect spot for your speakers that give you a clear focused sound, or perhaps allow a touch of a woolly sound if you want more of an old school sound (don't let it get too woolly or you'll still have over-excursion problems).
