Disclaimer: I'm going to be using the term "white dwarf" to refer to any spherical celestial body made of electron degenerate matter. If I had a better term, I would use it.
The Chandrasekhar limit for white dwarfs can be approximated with the equation $M_{limit}=\frac{\omega_3^0 \sqrt{3\pi}}{2} \left(\frac{\hbar c}{G}\right)^\frac32 \frac{1}{\left(\mu_e m_H\right)^2}$. The most relevant part of the equation here is $\frac{1}{\left(\mu_e m_H\right)^2}$. $m_H$ is the mass of a hydrogen atom and $\mu_e$ is the average molecular weight per electron, and it depends on what the white dwarf is made of. In real white dwarfs, $\mu_e$ is around 2, since the elements in a white dwarf have mostly equal numbers of protons and neutrons, so the Chandrasekhar limit is around 1.4 $M_\odot$.
But it seems like $\mu_e$, and therefore $M_{limit}$, could theoretically be very different if the white dwarf was made of different elements. If a white dwarf was (somehow) made of pure hydrogen, for example, $\mu_e$ would be basically 1, and $M_{limit}$ would evaluate to $5.7 M_\odot$. If a white dwarf was made of mercury-204, which has the highest mass-to-electron ratio among stable nuclei, $\mu_e$ would be around 2.55, and the Chandrasekhar for such a white dwarf would be around $0.88 M_\odot$. Therefore, it looks like the Chandrasekhar limit for any stable white dwarf would have to be between $0.88 M_\odot$ and $5.7 M_\odot$. Do I have this right? Obviously we'd never have a white dwarf made of hydrogen or mercury.