The Police in Phuket now have surveillance cameras in some of their police cars that detect overstayers in real time - not scaremongering, true fact. Do as Tod recommends
As a Thailand resident you can open an account with Saxo Bank in Singapore, who offer a wide selection of equities, ETFs, bonds, money market funds, managed funds etc from most countries you would be interested. Multiple currencies available. If you have any issues opening an account ping me and I have a contact there.
In comparison the Thai banks seem to offer retail products with horrendous hidden sales commissions, very Thailand oriented investments and of course a VIP card that gets you a special parking space at Central 😂😂