How many sata drives / total storage are you reaching for? If I remember correctly the 7040 sff has 4 internal sata ports, so I see 2 options depending on your needs:

• remove the dvd drive, replace with something like this: SATA Hard Drive Caddy, Universal... https://www.amazon.com/dp/B075846MD2?ref=ppx_pop_mob_ap_share

Then cram up to 3 more 2.5” into the drive bay.

• you should have a pcie 16x half-height bay. Get something like a LSI 8e HBA, and use that to plug in the drives in the external enclosure: https://www.ebay.com/itm/163534822734?epid=28034148027&hash=item26136f5d4e:g:5sEAAOSwdwlcX2E3

Keep in mind you’ll need a power source for the external drives as well. Not sure if there are good options to use the 7040’ internal PSU or not.

If it's a laptop, none of the above. I use a caddy:

https://www.amazon.com/Tray-Universal-12-7mm-Enclosures-ThinkPad/dp/B075846MD2/ref=sr_1_3?crid=1DI2AREYWUPOO&keywords=ssd+caddy&qid=1647873898&s=electronics&sprefix=ssd+caddy%2Celectronics%2C129&sr=1-3