Yes. There were some forms of rigid plate defenses used alongside maille in the 13th and early 14th centuries. However, this did not take the form later plate armour, where the armour is a nearly complete exoskeleton, but instead was made of smaller pieces.

The 13th century is the earlier I have seen reliable evidence of plate supplements of maille armour. It is important to remember that documentary evidence is often inexact, there is very little -physical- evidence from the 13th century surviving and pictorial evidence can be hard to decipher because knights of the 13th century are generally depicting wearing surcoats, which covers their torsos. It is possible that some of these defences came into use earlier than the surviving evidence indicates. That being said, we have at least to depictions of a surcoat reinforced with plate defenses or early coat of plates - the statue of St. Maurice that u/cnzmur metions below, and the reliquary that I mention below. In addition, we have some good documentary evidence for coats of plates - in 1295 the merchant Fereric the Lombard collected together together, among other things, 5067 coats of plates*. This would suggest that by the end of the 13th century some form of coat of plates was fairly common.

In the 13th century you also see couters (elbow defenses) and poleyns (knee defenses). You can see the poleyns in particular on effigies, such as this one There are also depictions of some form of rigid gauntlets in art, but most written sources mention whalebone, not iron, but there is a reference to iron gauntlets from the 1290's. So the primary defense in the 13th century is very much maille, but this is increasingly supplmented with plate.

If you use the Black Death as the 'High'/'Late' medieval cut off point, then you see some fairly sophisticated plate defenses for limbs develop by 1350 - there are effigies with all their limbs defended by plate armour by 1350, and they would have most likely worn some form of plate reinforcement on their body.

However, plate armour as we think of it - the exoskeleton I mention above, with a solid breastplate and articulated limb defenses - comes into use later, in the last quarter of the 14th century. An early depiction of this is the alterpiece of Pistoia Cathedral from around 1377. There is also one surviving late 14th century breastplate in the Bayerische Nationalmuseum in Munich (it was originally covered in velvet). So in the 14th century we see plate move from being a supplment to maille to replacing it as the primary defense for knights and gentlemen at arms.

Sources: Alan Williams, the Knight and the Blast Furnace

Edge and Paddock, Arms and Armour of the Medieval Knight

Images as cited

*This translation is via Williams, the Knight and the Blast Furnace.

In the 13th century, and even as early as the 12th, small pieces of plate armour were progressively incorporated into chainmail armour, including greaves, couters, spaulders, gauntlets and increasingly complex helmets, like the famous "great helm", commonly known as "crusader helm".

EDIT: I thought I had seen information in my ources regarding the beginning of the transition to plate armour in the 12th century, but I've taken another look to refresh my memory, and it seems I was wrong. Apparently the process began in the 13th century, juding form what I've seen.