Will the costs for a new apartment be covered if the new apartment is slightly more expensive than the previous one?

If a person who is entitled to benefits from an apartment with a previously reasonable cost of accommodation in another apartment, which is more expensive but still appropriate, then only the current reasonable costs will be assumed for the new apartment. This does not apply if the relocation is necessary.

Section § 22 Absatz 1 Satz 2 SGB II