This will greatly depend on your particular phone.

Apple

iPhones that support eSIM can store several profiles, but only two can be active at the same time and one of them can even be a physical SIM.

• iPhone 13 and newer: You can have two active eSIMs at once or one eSIM and one physical SIM.
• iPhone XS to iPhone 12: Only one eSIM can be active at a time, but you can still use it alongside a physical SIM.

Samsung

• Galaxy S24 series and newer (S24, S24+, S24 Ultra, Z Flip6, Z Fold6 and onwards): Two active eSIMs at the same time.
• Earlier models: Usually support one eSIM and one physical SIM.

Other Android devices
Most Android phones that support eSIM can store multiple profiles. In many cases, you can use one eSIM together with a physical SIM, similar to older iPhones and Samsung models.