The recently discovered thermally induced magnetization switching (TIMS) induced by single femtosecond laser pulses in ferrimagnetic GdFeCo alloys proceeds on the picosecond time-scale. The rate at which data can be changed for use of TIMS in technological devices is limited by the processes leading to thermal equilibrium. In the present work, we address the question of whether it is possible to further excite switching via TIMS well before thermal equilibrium between subsystems is reached. In particular, we investigate the conditions for double thermally induced magnetic switching by the application of two shortly delayed laser pulses. These conditions become relevant for potential applications as it sets both a limit to rewrite data and demonstrates the importance of spatial confinement of a heat pulse to bit size, as neighboring bits may be accidentally re-switched for spatially extended pulse spots. To demonstrate this effect, we theoretically study the switching behavior in a prototypical ferrimagnetic GdFeCo alloy as a function of composition. We use computer simulations based on thermal atomistic spin dynamics and demonstrate the possibility of inducing a second switching event well before thermal equilibrium is reached and define the conditions under which it can occur. Our theoretical findings could serve as a guidance for further understanding of TIMS as well as to act as a guide for future applications.