Yes, you can. Private contracts, as opposed to public contracts (the ones signed in front of Notaries) also have validity and completion force in what refers to any permissible condition they include and are perfectly binding for you and your seller.
However, according to the Spanish legal system these contracts have no legal effects for/against third parties not knowing that such contract exists, such as banks, creditors, tax authorities, claimants, etc. Bearing this in mind you would understand how important it is that a purchasing contract is made “public”, and in Spain this is only legally possible through a Notary’s “Escritura” jointly with the registry at the Property’s Registry of the town where the property is situated. By means of this Escritura and registry, there is no third party who can allege the contract has no effects for/against him.
In general terms it favours the employee since Spain has a strong protection of the worker’s rights and many “over the standard” conditions may apply according to the criterion of Labour Courts to contracts that do not formally define some of the basic conditions, even if the employer thought they were verbally agreed, such as the contract’s term of duration, number of salary payments in a year (12 vs. 14), etc. Our advice to the employer is to always have a written contract that could set those conditions in writing specially the ones that unless legally agreed by both parties have a higher protective level for the employee in case both parties did not state otherwise