People will tell you it is impossible and people will tell you they did it. Both are describing real experiences. What decides the outcome is mostly which two languages, and how far along you already are in each.
The real cost is time, not interference
Interference between languages is smaller than the folklore suggests, and it mostly shows up as the occasional wrong word rather than deep confusion. The genuine cost is arithmetic: two languages means each gets half the practice. If you had thirty minutes a day, you now have fifteen for each. That does not stop you learning — it doubles how long everything takes.
Similar pairs are harder, not easier
Two closely related languages — Spanish and Italian, Dutch and German — feel efficient because so much transfers. In practice they blur, especially in speaking, and you spend months untangling which ending belongs to which. A distant pair interferes far less. If you are set on two, pick ones with little in common.
Do not start both from zero
The version that usually works: one language is already past the beginner stage and in maintenance, the other is the one you are actively building. Maintenance is cheap; building is not. Two beginner languages at once is the combination that most often ends with neither reaching a usable level.
Split by block, not by day
If you do go ahead, give each language its own days rather than alternating within a session. Switching costs attention, and short blocks of one language beat interleaved fragments of two. Keep one as the priority. When the week goes badly and only one gets done, you want to know in advance which one that is.
Two at once is possible and it is slower. If you have a deadline for either of them, do one properly first.