Record clamp

It will not hurt your TT. you might get some SQ out of it.
just be careful not to over clamp it where the album starts to warp. If you don’t like it put it away, maybe on another TT.
I have been using a clamp on my TT’s for 40+ years.
My Oracle Delphi came with a clamp. My present TT Clear Audio Master Solution, I use a CA clamp.
Try different types of devices. Respectfully 
Joe

Another good one to try is OL Cartridge Enabler. While I hate the name the darn thing seems to work at least as good as and probably better than fO.q tape. The Enabler is made from some material he developed. It looks sort of like felt but clearly not, it is directional and even labeled so one side goes against the cartridge the other against the head shell. There are also washers made of the same material. The deal is you have the bolt, normal washer, Enabler washer, head shell, Enabler, cartridge. So the cartridge is effectively isolated from the head shell by the Enabler material.

The material is kind of squishy. After a while I was playing around and found the sound can be subtly tailored by slightly tweaking the torque. Like a small fraction of a turn. Does not like to be real tight.

Thanks for the tip. (No pun intended.)

While I haven't (and probably won't) try millercarbon's recommendation of the Origin Live One Gravity record weight, I have tried two tweaks on my Rega P8, which I plan on upgrading soon:  

Firstly, the P8 without any weight or clamp did have quite a bit of resonant sound, which muffled detail.  A record weight improved the detail noticeably.  A SOTA reflex record clamp markedly improved detail, clarity, etc to such a great degree that I'm not in so much of a hurry to upgrade my turntable now.  

I also placed the Rega P8 on different objects:  a walnut component stand, sitting on a concrete slab still left some background noise, which wasn't noticeable, until I placed the P8 on hockey pucks, whereafter, the noise floor dramatically dropped.  I then placed a sponge puck under the hockey puck, and the noise floor dropped more, and it is now quite silent.  

Now, all this does decrease the resonances, which Rega philosophically says are imporant to vinyl playback; however, in my system, these modifications definitely, and markedly improved the listening experience.